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Environment-limited transfer of angular momentum in Bose liquids
Authors:
Alberto Cappellaro,
Giacomo Bighin,
Igor Cherepanov,
Mikhail Lemeshko
Abstract:
Impurity motion in a many-body environment has been a central issue in the field of low-temperature physics for decades. In bosonic quantum fluids, the onset of a drag force experienced by point-like objects is due to collective environment excitations, driven by the exchange of linear momentum between the impurity and the many-body bath. In this work we consider a rotating impurity, with the aim…
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Impurity motion in a many-body environment has been a central issue in the field of low-temperature physics for decades. In bosonic quantum fluids, the onset of a drag force experienced by point-like objects is due to collective environment excitations, driven by the exchange of linear momentum between the impurity and the many-body bath. In this work we consider a rotating impurity, with the aim of exploring how angular momentum is exchanged with the surrounding bosonic environment. In order to elucidate this issues, we employ a quasiparticle approach based on the angulon theory, which allows us to effectively deal with the non-trivial algebra of quantized angular momentum in presence of a many-body environment. We uncover how impurity dressing by environmental excitations can establish an exchange channel, whose effectiveness crucially depends on the initial state of the impurity. Remarkably, we find that there is a critical value of initial angular momentum, above which this channel effectively freezes.
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Submitted 27 January, 2025;
originally announced January 2025.
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Finite-size effects in the two-dimensional BCS-BEC crossover
Authors:
M. Lanaro,
G. Bighin,
L. Dell'Anna,
L. Salasnich
Abstract:
We study the finite-size effects on the BCS-BEC crossover in two dimensions, occurring in confined fermionic superfluids. We analyze several thermodynamic properties, such as the chemical potential, the energy gap and the superfluid density, taking into account unavoidable quantum fluctuations, and, by means of renormalization group procedure, we detect the putative Berezinskii-Kosterlitz-Thouless…
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We study the finite-size effects on the BCS-BEC crossover in two dimensions, occurring in confined fermionic superfluids. We analyze several thermodynamic properties, such as the chemical potential, the energy gap and the superfluid density, taking into account unavoidable quantum fluctuations, and, by means of renormalization group procedure, we detect the putative Berezinskii-Kosterlitz-Thouless phase transition at finite-size.
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Submitted 9 March, 2024; v1 submitted 11 January, 2024;
originally announced January 2024.
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Non-equilibrium dynamics of dipolar polarons
Authors:
Artem G. Volosniev,
Giacomo Bighin,
Luis Santos,
Luis A. Peña Ardila
Abstract:
We study the out-of-equilibrium quantum dynamics of dipolar polarons, i.e., impurities immersed in a dipolar Bose-Einstein condensate, after a quench of the impurity-boson interaction. We show that the dipolar nature of the condensate and of the impurity results in anisotropic relaxation dynamics, in particular, anisotropic dressing of the polaron. More relevantly for cold-atom setups, quench dyna…
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We study the out-of-equilibrium quantum dynamics of dipolar polarons, i.e., impurities immersed in a dipolar Bose-Einstein condensate, after a quench of the impurity-boson interaction. We show that the dipolar nature of the condensate and of the impurity results in anisotropic relaxation dynamics, in particular, anisotropic dressing of the polaron. More relevantly for cold-atom setups, quench dynamics is strongly affected by the interplay between dipolar anisotropy and trap geometry. Our findings pave the way for simulating impurities in anisotropic media utilizing experiments with dipolar mixtures.
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Submitted 8 December, 2023; v1 submitted 29 May, 2023;
originally announced May 2023.
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Resonantly enhanced superconductivity mediated by spinor condensates
Authors:
Giacomo Bighin,
Puneet A. Murthy,
Nicolò Defenu,
Tilman Enss
Abstract:
Achieving strong interactions in fermionic many-body systems is a major theme of research in condensed matter physics. It is well-known that interactions between fermions can be mediated through a bosonic medium, such as a phonon bath or Bose-Einstein condensate (BEC). Here we show that such induced attraction can be resonantly enhanced when the bosonic medium is a two-component spinor BEC. The st…
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Achieving strong interactions in fermionic many-body systems is a major theme of research in condensed matter physics. It is well-known that interactions between fermions can be mediated through a bosonic medium, such as a phonon bath or Bose-Einstein condensate (BEC). Here we show that such induced attraction can be resonantly enhanced when the bosonic medium is a two-component spinor BEC. The strongest interaction is achieved by tuning the boson-boson scattering to the quantum critical spinodal point of the BEC where the sound velocity vanishes. The fermion pairing gap and the superconducting critical temperature can thus be dramatically enhanced. We propose two experimental realizations of this scenario, with exciton-polariton systems in two-dimensional semiconductors and ultracold atomic Bose-Fermi mixtures.
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Submitted 20 June, 2025; v1 submitted 14 December, 2022;
originally announced December 2022.
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Universal scaling in real dimension
Authors:
Giacomo Bighin,
Tilman Enss,
Nicolò Defenu
Abstract:
The concept of universality has shaped our understanding of many-body physics, but is mostly limited to homogenous systems. Here, we present a study of universality on a non-homogeneous graph, the long-range diluted graph (LRDG). Its scaling theory is controlled by a single parameter, the spectral dimension $d_{s}$, which plays the role of the relevant parameter on complex geometries. The graph un…
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The concept of universality has shaped our understanding of many-body physics, but is mostly limited to homogenous systems. Here, we present a study of universality on a non-homogeneous graph, the long-range diluted graph (LRDG). Its scaling theory is controlled by a single parameter, the spectral dimension $d_{s}$, which plays the role of the relevant parameter on complex geometries. The graph under consideration allows us to tune the value of the spectral dimension continuously also to noninteger values and to find the universal exponents as continuous functions of the dimension. By means of extensive numerical simulations, we probe the scaling exponents of a simple instance of $O(\mathcal{N})$ symmetric models on the LRDG showing quantitative agreement with the theoretical prediction of universal scaling in real dimensions.
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Submitted 19 May, 2024; v1 submitted 23 November, 2022;
originally announced November 2022.
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First and second sound in two-dimensional bosonic and fermionic superfluids
Authors:
L. Salasnich,
A. Cappellaro,
K. Furutani,
A. Tononi,
G. Bighin
Abstract:
We review our theoretical results about the sound propagation in two-dimensional (2D) systems of ultracold fermionic and bosonic atoms. In the superfluid phase, characterized by the spontaneous symmetry breaking of the $U(1)$ symmetry, there is the coexistence of first and second sound. In the case of weakly-interacting repulsive bosons, we model the recent measurements of the sound velocities of…
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We review our theoretical results about the sound propagation in two-dimensional (2D) systems of ultracold fermionic and bosonic atoms. In the superfluid phase, characterized by the spontaneous symmetry breaking of the $U(1)$ symmetry, there is the coexistence of first and second sound. In the case of weakly-interacting repulsive bosons, we model the recent measurements of the sound velocities of 39K atoms in 2D obtained in the weakly-interacting regime and around the Berezinskii-Kosterlitz-Thouless (BKT) superfluid-to-normal transition temperature. In particular, we perform a quite accurate computation of the superfluid density and show that it is reasonably consistent with the experiment. For superfluid attractive fermions, we calculate the first and second sound velocities across the whole BCS-BEC crossover. In the low-temperature regime we reproduce the recent measurements of first-sound speed with 6Li atoms. We also predict that only in the finite-temperature BEC regime there is mixing between sound modes.
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Submitted 18 October, 2022;
originally announced October 2022.
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Unitary Fermi superfluid near the critical temperature: thermodynamics and sound modes from elementary excitations
Authors:
G. Bighin,
A. Cappellaro,
L. Salasnich
Abstract:
We compare recent experimental results [Science 375, 528 (2022)] of the superfluid unitary Fermi gas near the critical temperature with a thermodynamic model based on elementary excitations of the system. We find very good agreement between experimental data and our theory for several quantities such as first sound, second sound, and superfluid fraction. We also show that mode mixing between first…
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We compare recent experimental results [Science 375, 528 (2022)] of the superfluid unitary Fermi gas near the critical temperature with a thermodynamic model based on elementary excitations of the system. We find very good agreement between experimental data and our theory for several quantities such as first sound, second sound, and superfluid fraction. We also show that mode mixing between first and second sound occurs. Finally, we characterize the response amplitude to a density perturbation: close to the critical temperature both first and second sound can be excited through a density perturbation, whereas at lower temperatures only the first sound mode exhibits a significant response.
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Submitted 8 June, 2022;
originally announced June 2022.
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Diagrammatic Monte Carlo for electronic correlation in molecules: high-order many-body perturbation theory with low scaling
Authors:
G. Bighin,
Q. P. Ho,
M. Lemeshko,
T. V. Tscherbul
Abstract:
We present a low-scaling diagrammatic Monte Carlo approach to molecular correlation energies. Using combinatorial graph theory to encode many-body Hugenholtz diagrams, we sample the Møller-Plesset (MPn) perturbation series, obtaining accurate correlation energies up to n = 5, with quadratic scaling in the number of basis functions. Our technique reduces the computational complexity of the molecula…
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We present a low-scaling diagrammatic Monte Carlo approach to molecular correlation energies. Using combinatorial graph theory to encode many-body Hugenholtz diagrams, we sample the Møller-Plesset (MPn) perturbation series, obtaining accurate correlation energies up to n = 5, with quadratic scaling in the number of basis functions. Our technique reduces the computational complexity of the molecular many-fermion correlation problem, opening up the possibility of low-scaling, accurate stochastic computations for a wide class of many-body systems described by Hugenholtz diagrams.
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Submitted 23 March, 2022;
originally announced March 2022.
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A simple model for high rotational excitations of molecules in a superfluid
Authors:
Igor N. Cherepanov,
Giacomo Bighin,
Constant A. Schouder,
Adam S. Chatterley,
Henrik Stapelfeldt,
Mikhail Lemeshko
Abstract:
We present a simple quantum mechanical model describing excited rotational states of molecules in superfluid helium nanodroplets, as recently studied in non-adiabatic molecular alignment experiments [Cherepanov et al., Phys. Rev. A 104, L061303 (2021)]. We show that a linear molecule immersed in a superfluid can be seen as an effective symmetric top, similar to the rotational structure of radicals…
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We present a simple quantum mechanical model describing excited rotational states of molecules in superfluid helium nanodroplets, as recently studied in non-adiabatic molecular alignment experiments [Cherepanov et al., Phys. Rev. A 104, L061303 (2021)]. We show that a linear molecule immersed in a superfluid can be seen as an effective symmetric top, similar to the rotational structure of radicals, such as OH or NO, but with the angular momentum of the superfluid playing the role of the electronic angular momentum in free molecules. The model allows to evaluate the effective rotational and centrifugal distortion constants for a broad range of species and to explain the crossover between light and heavy molecules in superfluid $^4$He in terms of the many-body wavefunction structure. Most important, the simple theory allows to answer the question as to what happens when the rotational angular momentum of the molecule increases beyond the lowest excited states accessible by infrared spectroscopy. Some of the above mentioned insights can be acquired by analyzing a simple 2x2 matrix.
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Submitted 31 January, 2022;
originally announced January 2022.
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An impurity in a heteronuclear two-component Bose mixture
Authors:
Giacomo Bighin,
Alessia Burchianti,
Francesco Minardi,
Tommaso Macrì
Abstract:
We study the fate of an impurity in an ultracold heteronuclear Bose mixture, focusing on the experimentally relevant case of a $^{41}$K-$^{87}$Rb mixture, with the impurity in a $^{41}$K hyperfine state. Our work provides a comprehensive description of an impurity in a BEC mixture with contact interactions across its phase diagram. We present results for the miscible and immiscible regimes, as wel…
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We study the fate of an impurity in an ultracold heteronuclear Bose mixture, focusing on the experimentally relevant case of a $^{41}$K-$^{87}$Rb mixture, with the impurity in a $^{41}$K hyperfine state. Our work provides a comprehensive description of an impurity in a BEC mixture with contact interactions across its phase diagram. We present results for the miscible and immiscible regimes, as well as for the impurity in a self-bound quantum droplet. Here, varying the interactions, we find novel, exotic states where the impurity localizes either at the center or at the surface of the droplet.
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Submitted 23 September, 2021; v1 submitted 15 September, 2021;
originally announced September 2021.
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Excited rotational states of molecules in a superfluid
Authors:
Igor N. Cherepanov,
Giacomo Bighin,
Constant A. Schouder,
Adam S. Chatterley,
Simon H. Albrechtsen,
Alberto Viñas Muñoz,
Lars Christiansen,
Henrik Stapelfeldt,
Mikhail Lemeshko
Abstract:
We combine experimental and theoretical approaches to explore excited rotational states of molecules embedded in helium nanodroplets using CS$_2$ and I$_2$ as examples. Laser-induced nonadiabatic molecular alignment is employed to measure spectral lines for rotational states extending beyond those initially populated at the 0.37 K droplet temperature. We construct a simple quantum mechanical model…
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We combine experimental and theoretical approaches to explore excited rotational states of molecules embedded in helium nanodroplets using CS$_2$ and I$_2$ as examples. Laser-induced nonadiabatic molecular alignment is employed to measure spectral lines for rotational states extending beyond those initially populated at the 0.37 K droplet temperature. We construct a simple quantum mechanical model, based on a linear rotor coupled to a single-mode bosonic bath, to determine the rotational energy structure in its entirety. The calculated and measured spectral lines are in good agreement. We show that the effect of the surrounding superfluid on molecular rotation can be rationalized by a single quantity -- the angular momentum, transferred from the molecule to the droplet.
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Submitted 30 June, 2021;
originally announced July 2021.
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Propagation of first and second sound in a two-dimensional Fermi superfluid
Authors:
A. Tononi,
A. Cappellaro,
G. Bighin,
L. Salasnich
Abstract:
Sound propagation is a macroscopic manifestation of the interplay between the equilibrium thermodynamics and the dynamical transport properties of fluids. Here, for a two-dimensional system of ultracold fermions, we calculate the first and second sound velocities across the whole BCS-BEC crossover and we analyze the system response to an external perturbation. In the low-temperature regime we repr…
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Sound propagation is a macroscopic manifestation of the interplay between the equilibrium thermodynamics and the dynamical transport properties of fluids. Here, for a two-dimensional system of ultracold fermions, we calculate the first and second sound velocities across the whole BCS-BEC crossover and we analyze the system response to an external perturbation. In the low-temperature regime we reproduce the recent measurements [Phys Rev. Lett. {\bf 124}, 240403 (2020)] of the first sound velocity, which, due to the decoupling of density and entropy fluctuations, is the sole mode excited by a density probe. Conversely, a heat perturbation excites only the second sound, which, being sensitive to the superfluid depletion, vanishes in the deep BCS regime, and jumps discontinuously to zero at the Berezinskii-Kosterlitz-Thouless superfluid transition. A mixing between the modes occurs only in the finite-temperature BEC regime, where our theory converges to the purely bosonic results.
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Submitted 20 July, 2021; v1 submitted 14 September, 2020;
originally announced September 2020.
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Intermolecular forces and correlations mediated by a phonon bath
Authors:
Xiang Li,
Enderalp Yakaboylu,
Giacomo Bighin,
Richard Schmidt,
Mikhail Lemeshko,
Andreas Deuchert
Abstract:
Inspired by the possibility to experimentally manipulate and enhance chemical reactivity in helium nanodroplets, we investigate the effective interaction and the resulting correlations between two diatomic molecules immersed in a bath of bosons. By analogy with the bipolaron, we introduce the \emph{biangulon} quasiparticle describing two rotating molecules that align with respect to each other due…
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Inspired by the possibility to experimentally manipulate and enhance chemical reactivity in helium nanodroplets, we investigate the effective interaction and the resulting correlations between two diatomic molecules immersed in a bath of bosons. By analogy with the bipolaron, we introduce the \emph{biangulon} quasiparticle describing two rotating molecules that align with respect to each other due to the effective attractive interaction mediated by the excitations of the bath. We study this system in different parameter regimes and apply several theoretical approaches to describe its properties. Using a Born-Oppenheimer approximation, we investigate the dependence of the effective intermolecular interaction on the rotational state of the two molecules. In the strong-coupling regime, a product-state ansatz shows that the molecules tend to have a strong alignment in the ground state. To investigate the system in the weak-coupling regime, we apply a one-phonon excitation variational ansatz, which allows us to access the energy spectrum. In comparison to the angulon quasiparticle, the biangulon shows shifted angulon instabilities and an additional spectral instability, where resonant angular momentum transfer between the molecules and the bath takes place. These features are proposed as an experimentally observable signature for the formation of the biangulon quasiparticle. Finally, by using products of single angulon and bare impurity wave functions as basis states, we introduce a diagonalization scheme that allows us to describe the transition from two separated angulons to a biangulon as a function of the distance between the two molecules.
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Submitted 5 December, 2019;
originally announced December 2019.
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BKT-paired phase in coupled XY models
Authors:
Giacomo Bighin,
Nicolò Defenu,
István Nándori,
Luca Salasnich,
Andrea Trombettoni
Abstract:
We study the effect of a linear tunneling coupling between 2D systems, each separately exhibiting the topological Berezinskii-Kosterlitz-Thouless (BKT) transition. In the uncoupled limit, there are two phases: one where the 1-body correlation functions are algebraically decaying and the other with exponential decay. When the linear coupling is turned on, a third BKT-paired phase emerges, in which…
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We study the effect of a linear tunneling coupling between 2D systems, each separately exhibiting the topological Berezinskii-Kosterlitz-Thouless (BKT) transition. In the uncoupled limit, there are two phases: one where the 1-body correlation functions are algebraically decaying and the other with exponential decay. When the linear coupling is turned on, a third BKT-paired phase emerges, in which 1-body correlations are exponentially decaying, while 2-body correlation functions exhibit power-law decay. We perform numerical simulations in the paradigmatic case of two coupled XY models at finite temperature, finding that for any finite value of the interlayer coupling, the BKT-paired phase is present. We provide a picture of the phase diagram using a renormalization group approach.
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Submitted 14 July, 2019;
originally announced July 2019.
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Detecting composite orders in layered models via machine learning
Authors:
W. Rzadkowski,
N. Defenu,
S. Chiacchiera,
A. Trombettoni,
G. Bighin
Abstract:
Determining the phase diagram of systems consisting of smaller subsystems 'connected' via a tunable coupling is a challenging task relevant for a variety of physical settings. A general question is whether new phases, not present in the uncoupled limit, may arise. We use machine learning to study layered spin models, in which the spin variables constituting each of the uncoupled systems (to which…
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Determining the phase diagram of systems consisting of smaller subsystems 'connected' via a tunable coupling is a challenging task relevant for a variety of physical settings. A general question is whether new phases, not present in the uncoupled limit, may arise. We use machine learning to study layered spin models, in which the spin variables constituting each of the uncoupled systems (to which we refer as layers) are coupled to each other via an interlayer coupling. In such systems, in general, composite order parameters involving spins of different layers may emerge as a consequence of the interlayer coupling. We focus on the layered Ising and Ashkin-Teller models as a paradigmatic case study, determining their phase diagram via the application of a machine learning algorithm to the Monte Carlo data. Remarkably our technique is able to correctly characterize all the system phases also in the case of hidden order parameters, i.e., order parameters whose expression in terms of the microscopic configurations would require additional preprocessing of the data fed to the algorithm. We correctly retrieve the three known phases of the Ashkin-Teller model with ferromagnetic couplings, including the phase described by a composite order parameter. For the bilayer and trilayer Ising models the phases we find are only the ferromagnetic and the paramagnetic ones. Within the approach we introduce, owing to the construction of convolutional neural networks, naturally suitable for layered image-like data with arbitrary number of layers, no preprocessing of the Monte Carlo data is needed, also with regard to its spatial structure. The physical meaning of our results is discussed and compared with analytical data, where available. Yet, the method can be used without any a priori knowledge of the phases one seeks to find and can be applied to other models and structures.
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Submitted 28 April, 2020; v1 submitted 11 July, 2019;
originally announced July 2019.
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Far-from-equilibrium dynamics of angular momentum in a quantum many-particle system
Authors:
Igor N. Cherepanov,
Giacomo Bighin,
Lars Christiansen,
Anders Vestergaard Jørgensen,
Richard Schmidt,
Henrik Stapelfeldt,
Mikhail Lemeshko
Abstract:
We use laser-induced rotation of single molecules embedded in superfluid helium nanodroplets to reveal angular momentum dynamics and transfer in a controlled setting, under far-from-equilibrium conditions. As an unexpected result, we observe pronounced oscillations of time-dependent molecular alignment that have no counterpart in gas-phase molecules. Angulon theory reveals that these oscillations…
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We use laser-induced rotation of single molecules embedded in superfluid helium nanodroplets to reveal angular momentum dynamics and transfer in a controlled setting, under far-from-equilibrium conditions. As an unexpected result, we observe pronounced oscillations of time-dependent molecular alignment that have no counterpart in gas-phase molecules. Angulon theory reveals that these oscillations originate from the unique rotational structure of molecules in He droplets and quantum-state-specific transfer of rotational angular momentum to the many-body He environment on picosecond timescales. Our results pave the way to understanding collective effects of macroscopic angular momentum exchange in solid state systems in a bottom-up fashion.
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Submitted 8 July, 2019; v1 submitted 28 June, 2019;
originally announced June 2019.
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Variational approaches to quantum impurities: from the Fröhlich polaron to the angulon
Authors:
Xiang Li,
Giacomo Bighin,
Enderalp Yakaboylu,
Mikhail Lemeshko
Abstract:
Problems involving quantum impurities, in which one or a few particles are interacting with a macroscopic environment, represent a pervasive paradigm, spanning across atomic, molecular, and condensed-matter physics. In this paper we introduce new variational approaches to quantum impurities and apply them to the Fröhlich polaron -- a quasiparticle formed out of an electron (or other point-like imp…
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Problems involving quantum impurities, in which one or a few particles are interacting with a macroscopic environment, represent a pervasive paradigm, spanning across atomic, molecular, and condensed-matter physics. In this paper we introduce new variational approaches to quantum impurities and apply them to the Fröhlich polaron -- a quasiparticle formed out of an electron (or other point-like impurity) in a polar medium, and to the angulon -- a quasiparticle formed out of a rotating molecule in a bosonic bath. We benchmark these approaches against established theories, evaluating their accuracy as a function of the impurity-bath coupling.
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Submitted 14 December, 2018; v1 submitted 24 October, 2018;
originally announced October 2018.
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Diagrammatic Monte Carlo approach to angular momentum in quantum many-particle systems
Authors:
G. Bighin,
T. V. Tscherbul,
M. Lemeshko
Abstract:
We introduce a Diagrammatic Monte Carlo (DiagMC) approach to angular momentum properties of quantum many-particle systems possessing a macroscopic number of degrees of freedom. The treatment is based on a diagrammatic expansion that merges the usual Feynman diagrams with the angular momentum diagrams known from atomic and nuclear structure theory, thereby incorporating the non-Abelian algebra inhe…
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We introduce a Diagrammatic Monte Carlo (DiagMC) approach to angular momentum properties of quantum many-particle systems possessing a macroscopic number of degrees of freedom. The treatment is based on a diagrammatic expansion that merges the usual Feynman diagrams with the angular momentum diagrams known from atomic and nuclear structure theory, thereby incorporating the non-Abelian algebra inherent to quantum rotations. Our approach is applicable at arbitrary coupling, is free of systematic errors and of finite size effects, and naturally provides access to the impurity Green function. We exemplify the technique by obtaining an all-coupling solution of the angulon model, however, the method is quite general and can be applied to a broad variety of systems in which particles exchange quantum angular momentum with their many-body environment.
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Submitted 1 October, 2018; v1 submitted 21 March, 2018;
originally announced March 2018.
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Renormalization of the superfluid density in the two-dimensional BCS-BEC crossover
Authors:
G. Bighin,
L. Salasnich
Abstract:
We analyze the theoretical derivation of the beyond-mean-field equation of state for a two-dimensional gas of dilute, ultracold alkali-metal atoms in the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover. We show that at zero temperature our theory -- considering Gaussian fluctuations on top of the mean-field equation of state -- is in very good agreement with experimenta…
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We analyze the theoretical derivation of the beyond-mean-field equation of state for a two-dimensional gas of dilute, ultracold alkali-metal atoms in the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover. We show that at zero temperature our theory -- considering Gaussian fluctuations on top of the mean-field equation of state -- is in very good agreement with experimental data. Subsequently, we investigate the superfluid density at finite temperature and its renormalization due to the proliferation of vortex-antivortex pairs. By doing so, we determine the Berezinskii-Kosterlitz-Thouless (BKT) critical temperature -- at which the renormalized superfluid density jumps to zero -- as a function of the inter-atomic potential strength. We find that the Nelson-Kosterlitz criterion overestimates the BKT temperature with respect to the renormalization group equations, this effect being particularly relevant in the intermediate regime of the crossover.
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Submitted 30 October, 2017;
originally announced October 2017.
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Diagrammatic approach to orbital quantum impurities interacting with a many-particle environment
Authors:
Giacomo Bighin,
Mikhail Lemeshko
Abstract:
Recently it was shown that an impurity exchanging orbital angular momentum with a surrounding bath can be described in terms of the angulon quasiparticle [Phys. Rev. Lett. 118, 095301 (2017)]. The angulon consists of a quantum rotor dressed by a many-particle field of boson excitations, and can be formed out of, for example, a molecule or a nonspherical atom in superfluid helium, or out of an elec…
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Recently it was shown that an impurity exchanging orbital angular momentum with a surrounding bath can be described in terms of the angulon quasiparticle [Phys. Rev. Lett. 118, 095301 (2017)]. The angulon consists of a quantum rotor dressed by a many-particle field of boson excitations, and can be formed out of, for example, a molecule or a nonspherical atom in superfluid helium, or out of an electron coupled to lattice phonons or a Bose condensate. Here we develop an approach to the angulon based on the path-integral formalism, which sets the ground for a systematic, perturbative treatment of the angulon problem. The resulting perturbation series can be interpreted in terms of Feynman diagrams, from which, in turn, one can derive a set of diagrammatic rules. These rules extend the machinery of the graphical theory of angular momentum - well known from theoretical atomic spectroscopy - to the case where an environment with an infinite number of degrees of freedom is present. In particular, we show that each diagram can be interpreted as a 'skeleton', which enforces angular momentum conservation, dressed by an additional many-body contribution. This connection between the angulon theory and the graphical theory of angular momentum is particularly important as it allows to systematically and substantially simplify the analytical representation of each diagram. In order to exemplify the technique, we calculate the 1- and 2-loop contributions to the angulon self-energy, the spectral function, and the quasiparticle weight. The diagrammatic theory we develop paves the way to investigate next-to-leading order quantities in a more compact way compared to the variational approaches.
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Submitted 10 August, 2017; v1 submitted 9 April, 2017;
originally announced April 2017.
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Vortices and antivortices in two-dimensional ultracold Fermi gases
Authors:
G. Bighin,
L. Salasnich
Abstract:
Vortices are commonly observed in the context of classical hydrodynamics: from whirlpools after stirring the coffee in a cup to a violent atmospheric phenomenon such as a tornado, all classical vortices are characterized by an arbitrary circulation value of the local velocity field. On the other hand the appearance of vortices with quantized circulation represents one of the fundamental signatures…
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Vortices are commonly observed in the context of classical hydrodynamics: from whirlpools after stirring the coffee in a cup to a violent atmospheric phenomenon such as a tornado, all classical vortices are characterized by an arbitrary circulation value of the local velocity field. On the other hand the appearance of vortices with quantized circulation represents one of the fundamental signatures of macroscopic quantum phenomena. In two-dimensional superfluids quantized vortices play a key role in determining finite-temperature properties, as the superfluid phase and the normal state are separated by a vortex unbinding transition, the Berezinskii-Kosterlitz-Thouless transition. Very recent experiments with two-dimensional superfluid fermions motivate the present work: we present theoretical results based on the renormalization group showing that the universal jump of the superfluid density and the critical temperature crucially depend on the interaction strength, providing a strong benchmark for forthcoming investigations.
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Submitted 7 March, 2017;
originally announced March 2017.
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Quantum fluctuations and vortex-antivortex unbinding in the 2D BCS-BEC crossover
Authors:
L. Salasnich,
G. Bighin
Abstract:
Very recently quasi two-dimensional (2D) systems made of attractive fermionic alkali-metal atoms with a widely tunable interaction due to Fano-Feshbach resonances have been realized. In this way it has been achieved the 2D crossover from the Bardeen-Cooper-Schrieffer regime of weakly-interacting Cooper pairs to the Bose-Einstein condensate regime strongly bound dimers. These experiments pave the w…
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Very recently quasi two-dimensional (2D) systems made of attractive fermionic alkali-metal atoms with a widely tunable interaction due to Fano-Feshbach resonances have been realized. In this way it has been achieved the 2D crossover from the Bardeen-Cooper-Schrieffer regime of weakly-interacting Cooper pairs to the Bose-Einstein condensate regime strongly bound dimers. These experiments pave the way to the investigation of 2D strongly-interacting attractive fermions during the Berezinskii-Kosterlitz-Thouless (BKT) transition from a low-temperature superfluid phase characterized by quasi-condensation to a high-temperature normal phase, where vortex proliferation driven by quantum and thermal fluctuations completely destroys superfluidity. In this paper we discuss our preliminar theoretical results on the behavior of the BKT critical temperature across the crossover. Our microscopic calculations are based on functional integration taking into account renormalized Gaussian fluctuations and the crucial 2D effect of vortex-antivortex unbinding.
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Submitted 1 November, 2016;
originally announced November 2016.
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Superfluid density in cuprates: hints on gauge compositeness of the holes
Authors:
P. A. Marchetti,
G. Bighin
Abstract:
We show that several features (the three-dimensional XY universality for moderate underdoping, the almost-BCS behaviour for moderate overdoping and the critical exponent) of the superfluid density in hole-doped cuprates hint at a composite structure of the holes. This idea can be implemented in a spin-charge gauge approach to the $t - t' - J$ model and provides indeed good agreement with available…
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We show that several features (the three-dimensional XY universality for moderate underdoping, the almost-BCS behaviour for moderate overdoping and the critical exponent) of the superfluid density in hole-doped cuprates hint at a composite structure of the holes. This idea can be implemented in a spin-charge gauge approach to the $t - t' - J$ model and provides indeed good agreement with available experimental data.
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Submitted 13 July, 2016;
originally announced July 2016.
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Universality in cuprates: a gauge approach
Authors:
P. A. Marchetti,
G. Bighin
Abstract:
In high-$T_c$ cuprates many quantities exhibit a non-Fermi liquid universality hinting at a very peculiar structure of the underlying pairing mechanism for superconductivity: in this work we focus on the universality for the in-plane resistivity and for the superfluid density.
We outline the previously developed spin-charge gauge approach to superconductivity in hole-doped cuprates: we decompose…
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In high-$T_c$ cuprates many quantities exhibit a non-Fermi liquid universality hinting at a very peculiar structure of the underlying pairing mechanism for superconductivity: in this work we focus on the universality for the in-plane resistivity and for the superfluid density.
We outline the previously developed spin-charge gauge approach to superconductivity in hole-doped cuprates: we decompose the hole of the $t-t'-J$ model for the $\mathrm{Cu}\mathrm{O}_2$ planes as the product of a spinful, chargeless gapped spinon and of a spinless, charged holon with Fermi surface. Each one of these particle excitations is bound to a statistical gauge flux, allowing one to optimize their statistics.
We show that this model allows for a natural interpretation of the universality: within this approach, under suitable conditions, the spinonic and holonic contributions to a response function sum up according to a Ioffe-Larkin rule. We argue that, if the spinonic contribution dominates, then one should expect strongly non-Fermi-liquid-like universality, due to the insensitivity of spinons to Fermi surface details. The in-plane resistivity and superfluid density are indeed dominated by the spinons in the underdoped region. We theoretically derive these quantities, discussing their universal behaviours and comparing them with experimental data.
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Submitted 4 May, 2016; v1 submitted 29 February, 2016;
originally announced February 2016.
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Gaussian fluctuations in the two-dimensional BCS-BEC crossover: finite temperature properties
Authors:
G Bighin,
L Salasnich
Abstract:
The role of fluctuations is enhanced in lower dimensionality systems: in a two dimensions off-diagonal long-range order is destroyed by the fluctuations at any finite temperature, drastically modifying the critical properties with respect to the three-dimensional counterpart. Recently two-dimensional systems of interacting fermions have been the subject of Montecarlo studies and experimental inves…
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The role of fluctuations is enhanced in lower dimensionality systems: in a two dimensions off-diagonal long-range order is destroyed by the fluctuations at any finite temperature, drastically modifying the critical properties with respect to the three-dimensional counterpart. Recently two-dimensional systems of interacting fermions have been the subject of Montecarlo studies and experimental investigations, in particular an ultracold gas of attractive fermions with a widely tunable interaction due to a Feshbach resonance has been realized and the Berezinskii-Kosterlitz-Thouless transition has been observed.
The present work deals with the theoretical description of an ultracold Fermi gas: we discuss the role of Gaussian fluctuations of the order parameter in the equation of state, in particular we take into account the first sound velocity, showing that the inclusion of order parameter fluctuations is needed in order to get the correct composite-boson limit in the strong-coupling regime. The theory is also compared with experimental data. Finally we focus on the superfluid density in the weak-coupling, intermediate and strong-coupling regimes at finite temperature, through which the Berezinskii-Kosterlitz-Thouless critical temperature is obtained.
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Submitted 16 February, 2016; v1 submitted 11 February, 2016;
originally announced February 2016.
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Beliaev damping of the Goldstone mode in atomic Fermi superfluids
Authors:
G. Bighin,
L. Salasnich,
P. A. Marchetti,
F. Toigo
Abstract:
Beliaev damping in a superfluid is the decay of a collective excitation into two lower frequency collective excitations; it represents the only decay mode for a bosonic collective excitation in a superfluid at T = 0. The standard treatment for this decay assumes a linear spectrum, which in turn implies that the final state momenta must be collinear to the initial state. We extend this treatment, s…
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Beliaev damping in a superfluid is the decay of a collective excitation into two lower frequency collective excitations; it represents the only decay mode for a bosonic collective excitation in a superfluid at T = 0. The standard treatment for this decay assumes a linear spectrum, which in turn implies that the final state momenta must be collinear to the initial state. We extend this treatment, showing that the inclusion of a gradient term in the Hamiltonian yields a realistic spectrum for the bosonic excitations; we then derive a formula for the decay rate of such excitations, and show that even moderate nonlinearities in the spectrum can yield substantial deviations from the standard result. We apply our result to an attractive Fermi gas in the BCS-BEC crossover: here the low-energy bosonic collective excitations are density oscillations driven by the phase of the pairing order field. These collective excitations, which are gapless modes as a consequence of the Goldstone mechanism, have a spectrum which is well established both theoretically and experimentally, and whose linewidth, we show, is determined at low temperatures by the Beliaev decay mechanism.
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Submitted 30 July, 2015;
originally announced July 2015.
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Finite-temperature quantum fluctuations in two-dimensional Fermi superfluids
Authors:
G. Bighin,
L. Salasnich
Abstract:
In two-dimensional systems with a continuous symmetry the Mermin-Wagner-Hohenberg theorem precludes spontaneous symmetry breaking and condensation at finite temperature. The Berezinskii-Kosterlitz-Thouless critical temperature marks the transition from a superfluid phase characterized by quasi-condensation and algebraic long-range order to a normal phase, where vortex proliferation completely dest…
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In two-dimensional systems with a continuous symmetry the Mermin-Wagner-Hohenberg theorem precludes spontaneous symmetry breaking and condensation at finite temperature. The Berezinskii-Kosterlitz-Thouless critical temperature marks the transition from a superfluid phase characterized by quasi-condensation and algebraic long-range order to a normal phase, where vortex proliferation completely destroys superfluidity. As opposed to conventional off-diagonal long-range order typical of three-dimensional superfluid systems, algebraic long-range order is driven by quantum and thermal fluctuations strongly enhanced in reduced dimensionality. Motivated by this unique scenario and by the very recent experimental realization of trapped quasi-two-dimensional fermionic clouds, we include one-loop Gaussian fluctuations in the theoretical description of resonant Fermi superfluids in two dimensions demonstrating that first sound, second sound and also critical temperature are strongly renormalized, away from their mean-field values. In particular, we prove that in the intermediate and strong coupling regimes these quantities are radically different when Gaussian fluctuations are taken into account. Our one-loop theory shows good agreement with very recent experimental data on the Berezinskii-Kosterlitz-Thouless critical temperature [Phys. Rev. Lett. 115, 010401 (2015)] and on the first sound velocity, giving novel predictions for the second sound as a function of interaction strength and temperature, open for experimental verification.
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Submitted 14 January, 2016; v1 submitted 27 July, 2015;
originally announced July 2015.
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Scattering length of composite bosons in the 3D BCS-BEC crossover
Authors:
L. Salasnich,
G. Bighin
Abstract:
We study the zero-temperature grand potential of a three-dimensional superfluid made of ultracold fermionic alkali-metal atoms in the BCS-BEC crossover. In particular, we analyze the zero-point energy of both fermionic single-particle excitations and bosonic collective excitations. The bosonic elementary excitations, which are crucial to obtain a reliable equation of state in the BEC regime, are o…
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We study the zero-temperature grand potential of a three-dimensional superfluid made of ultracold fermionic alkali-metal atoms in the BCS-BEC crossover. In particular, we analyze the zero-point energy of both fermionic single-particle excitations and bosonic collective excitations. The bosonic elementary excitations, which are crucial to obtain a reliable equation of state in the BEC regime, are obtained with a low-momentum expansion up to the forth order of the quadratic (Gaussian) action of the fluctuating pairing field. By performing a cutoff regularization and renormalization of Gaussian fluctuations, we find that the scattering length $a_B$ of composite bosons, bound states of fermionic pairs, is given by $a_B = (2/3) a_F$, where $a_F$ is the scattering length of fermions.
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Submitted 23 February, 2015;
originally announced February 2015.
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Gauge approach to superfluid density in underdoped cuprates
Authors:
P. A. Marchetti,
G. Bighin
Abstract:
We prove that a gauge approach based on a composite structure of the hole in hole-doped cuprates is able to capture analytically many features of the experimental data on superfluid density in the moderate-underdoping to nearly-optimal doping region, including critical exponent, the Uemura relation and near universality of the normalized superfluid density.
We prove that a gauge approach based on a composite structure of the hole in hole-doped cuprates is able to capture analytically many features of the experimental data on superfluid density in the moderate-underdoping to nearly-optimal doping region, including critical exponent, the Uemura relation and near universality of the normalized superfluid density.
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Submitted 11 May, 2015; v1 submitted 14 January, 2015;
originally announced January 2015.
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Pair condensation of polarized fermions in the BCS-BEC crossover
Authors:
G. Bighin,
L. Salasnich,
G. Mazzarella,
L. Dell'Anna
Abstract:
We investigate a two-component Fermi gas with unequal spin populations along the BCS-BEC crossover. By using the extended BCS equations and the concept of off-diagonal-long-range-order we derive a formula for the condensate number of Cooper pairs as a function of energy gap, average chemical potential, imbalance chemical potential and temperature. Then we study the zero-temperature condensate frac…
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We investigate a two-component Fermi gas with unequal spin populations along the BCS-BEC crossover. By using the extended BCS equations and the concept of off-diagonal-long-range-order we derive a formula for the condensate number of Cooper pairs as a function of energy gap, average chemical potential, imbalance chemical potential and temperature. Then we study the zero-temperature condensate fraction of Cooper pairs by varying interaction strength and polarization, finding a depletion of the condensate fraction by increasing the population imbalance. We also consider explicitly the presence of an external harmonic confinement and we study, within the local-density approximation, the phase separation between superfluid and normal phase regions of the polarized fermionic cloud. In particular, we calculate both condensate density profiles and total density profiles from the inner superfluid core to the normal region passing for the interface, where a finite jump in the density is a clear manifestation of this phase-separated regime. Finally, we compare our theoretical results with the available experimental data on the condensate fraction of polarized 6Li atoms [Science 311, 492 (2006)]. These experimental data are in reasonable agreement with our predictions in a suitable range of polarizations, but only in the BCS side of the crossover up to unitarity.
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Submitted 22 August, 2014; v1 submitted 11 April, 2014;
originally announced April 2014.