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Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions
Authors:
Y R Kartik,
Jhih-Shih You,
H. H. Jen
Abstract:
The geometry of quantum states can be an indicator of criticality, yet it remains less explored under non-Hermitian topological conditions. In this work, we unveil diverse scalings of the quantum geometry over the ground state manifold close to different topological phase transitions in a non-Hermitian long-range extension of the Kitaev chain. The derivative of the geometric phase, as well as its…
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The geometry of quantum states can be an indicator of criticality, yet it remains less explored under non-Hermitian topological conditions. In this work, we unveil diverse scalings of the quantum geometry over the ground state manifold close to different topological phase transitions in a non-Hermitian long-range extension of the Kitaev chain. The derivative of the geometric phase, as well as its scaling behavior, shows that systems with different long-range couplings can belong to distinct universality classes. Near certain criticalities, we further find that the Wannier state correlation function associated with extended Berry connection of the ground state exhibits spatially anomalous behaviors. Finally, we analyze the scaling of the quantum geometric tensor near phase transitions across exceptional points, shedding light on the emergence of novel universality classes.
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Submitted 5 May, 2025;
originally announced May 2025.
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Photon-mediated dipole-dipole interactions as a resource for quantum science and technology in cold atoms
Authors:
H. H. Jen
Abstract:
Photon-mediated dipole-dipole interactions arise from atom-light interactions, which are universal and prevalent in a wide range of open quantum systems. This pairwise and long-range spin-exchange interaction results from multiple light scattering among the atoms. A recent surge of interests and progresses in both experiments and theories promises this core mechanism of collective interactions as…
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Photon-mediated dipole-dipole interactions arise from atom-light interactions, which are universal and prevalent in a wide range of open quantum systems. This pairwise and long-range spin-exchange interaction results from multiple light scattering among the atoms. A recent surge of interests and progresses in both experiments and theories promises this core mechanism of collective interactions as a resource to study quantum science and to envision next-generation applications in quantum technology. Here we summarize recent developments in both theories and experiments, where we introduce several central theoretical approaches and focus on cooperative light scattering from small sample of free-space atoms, an atom-waveguide coupled interface that hosts the waveguide QED, and topological quantum optical platforms. The aim of this review is to manifest the essential and distinct features of collective dynamics induced by resonant dipole-dipole interactions and to reveal unprecedented opportunities in enhancing the performance or offering new applications in light manipulations, quantum metrology, quantum computations, and light harvesting innovations.
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Submitted 27 October, 2024;
originally announced October 2024.
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Atomic excitation trapping in dissimilar chirally-coupled atomic arrays
Authors:
I Gusti Ngurah Yudi Handayana,
Chun-Chi Wu,
Sumit Goswami,
Ying-Cheng Chen,
H. H. Jen
Abstract:
Atomic array coupled to a one-dimensional nanophotonic waveguide allows photon-mediated dipole-dipole interactions and nonreciprocal decay channels, which hosts many intriguing quantum phenomena owing to its distinctive and emergent quantum correlations. In this atom-waveguide quantum system, we theoretically investigate the atomic excitation dynamics and its transport property, specifically at an…
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Atomic array coupled to a one-dimensional nanophotonic waveguide allows photon-mediated dipole-dipole interactions and nonreciprocal decay channels, which hosts many intriguing quantum phenomena owing to its distinctive and emergent quantum correlations. In this atom-waveguide quantum system, we theoretically investigate the atomic excitation dynamics and its transport property, specifically at an interface of dissimilar atomic arrays with different interparticle distances. We find that the atomic excitation dynamics hugely depends on the interparticle distances of dissimilar arrays and the directionality of nonreciprocal couplings. By tuning these parameters, a dominant excitation reflection can be achieved at the interface of the arrays in the single excitation case. We further study two effects on the transport property-of external drive and of single excitation delocalization over multiple atoms, where we manifest a rich interplay between multi-site excitation and the relative phase in determining the transport properties. Finally, we present an intriguing trapping effect of atomic excitation by designing multiple zones of dissimilar arrays. Similar to the single excitations, multiple excitations are reflected from the array interfaces and trapped as well, although complete trapping of many excitations together is relatively challenging at long time due to a faster combined decay rate. Our results can provide insights to nonequilibrium quantum dynamics in dissimilar arrays and shed light on confining and controlling quantum registers useful for quantum information processing.
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Submitted 26 January, 2024; v1 submitted 10 November, 2023;
originally announced November 2023.
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Generating scalable graph states in an atom-nanophotonic interface
Authors:
C. -H. Chien,
S. Goswami,
C. -C. Wu,
W. -S. Hiew,
Y. -C. Chen,
H. H. Jen
Abstract:
Scalable graph states are essential for measurement-based quantum computation and many entanglement-assisted applications in quantum technologies. Generation of these multipartite entangled states requires a controllable and efficient quantum device with delicate design of generation protocol. Here we propose to prepare high-fidelity and scalable graph states in one and two dimensions, which can b…
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Scalable graph states are essential for measurement-based quantum computation and many entanglement-assisted applications in quantum technologies. Generation of these multipartite entangled states requires a controllable and efficient quantum device with delicate design of generation protocol. Here we propose to prepare high-fidelity and scalable graph states in one and two dimensions, which can be tailored in an atom-nanophotonic cavity via state carving technique. We propose a systematic protocol to carve out unwanted state components, which facilitates scalable graph states generations via adiabatic transport of a definite number of atoms in optical tweezers. An analysis of state fidelity is also presented, and the state preparation probability can be optimized via multiqubit state carvings and sequential single-photon probes. Our results showcase the capability of an atom-nanophotonic interface for creating graph states and pave the way toward novel problem-specific applications using scalable high-dimensional graph states with stationary qubits.
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Submitted 5 October, 2023;
originally announced October 2023.
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Scaling laws for non-Hermitian skin effect with long-range couplings
Authors:
Yi-Cheng Wang,
H. H. Jen,
Jhih-Shih You
Abstract:
Recent years have witnessed a surge of research on the non-Hermitian skin effect (NHSE) in one-dimensional lattices with finite-range couplings. In this work, we show that the long-range couplings that decay as $1/l^α$ at distance $l$ can fundamentally modify the behavior of NHSE and the scaling of quantum entanglement in the presence of nonreciprocity. At $α=0$, the nonlocality of couplings gives…
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Recent years have witnessed a surge of research on the non-Hermitian skin effect (NHSE) in one-dimensional lattices with finite-range couplings. In this work, we show that the long-range couplings that decay as $1/l^α$ at distance $l$ can fundamentally modify the behavior of NHSE and the scaling of quantum entanglement in the presence of nonreciprocity. At $α=0$, the nonlocality of couplings gives rise to the scale-free skin modes, whose localization length is proportional to the system size. Increasing the exponent $α$ drives a complex-to-real spectral transition and a crossover from a scale-free to constant localization length. Furthermore, the scaling of nonequilibrium steady-state entanglement entropy exhibits a subextensive law due to the nonlocality and the complex spectrum, in contrast to an area law arising from NHSE. Our results provide a theoretical understanding on the interplay between long-range couplings and non-Hermiticity.
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Submitted 2 April, 2023; v1 submitted 29 November, 2022;
originally announced November 2022.
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Non-Hermitian skin effects on many-body localized and thermal phases
Authors:
Yi-Cheng Wang,
Kuldeep Suthar,
H. H. Jen,
Yi-Ting Hsu,
Jhih-Shih You
Abstract:
Localization in one-dimensional interacting systems can be caused by disorder potentials or non-Hermiticity. The former phenomenon is the many-body localization (MBL), and the latter is the many-body non-Hermitian skin effect (NHSE). In this work, we numerically investigate the interplay between these two kinds of localization, where the energy-resolved MBL arises from a deterministic quasiperiodi…
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Localization in one-dimensional interacting systems can be caused by disorder potentials or non-Hermiticity. The former phenomenon is the many-body localization (MBL), and the latter is the many-body non-Hermitian skin effect (NHSE). In this work, we numerically investigate the interplay between these two kinds of localization, where the energy-resolved MBL arises from a deterministic quasiperiodic potential in a fermionic chain. We propose a set of eigenstate properties and long-time dynamics that can collectively distinguish the two localization mechanisms in the presence of non-Hermiticity. By computing the proposed diagnostics, we show that the thermal states are vulnerable to the many-body NHSE while the MBL states remain resilient up to a strong non-Hermiticity. Finally, we discuss experimental observables that can probe the difference between the two localizations in a non-Hermitian quasiperiodic fermionic chain. Our results pave the way toward experimental observations on the interplay of interaction, quasiperiodic potential, and non-Hermiticity.
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Submitted 11 January, 2023; v1 submitted 24 October, 2022;
originally announced October 2022.
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Non-Hermitian Many-Body Localization with Open Boundaries
Authors:
Kuldeep Suthar,
Yi-Cheng Wang,
Yi-Ping Huang,
H. H. Jen,
Jhih-Shih You
Abstract:
The explorations of non-Hermiticity have been devoted to investigate the disorder-induced many-body localization (MBL). However, the sensitivity of the spatial boundary conditions and the interplay of the non-Hermitian skin effect with many-body phenomena are not yet clear. For a MBL system in the presence of non-reciprocal tunnelings and random disorder potential, we identify two different comple…
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The explorations of non-Hermiticity have been devoted to investigate the disorder-induced many-body localization (MBL). However, the sensitivity of the spatial boundary conditions and the interplay of the non-Hermitian skin effect with many-body phenomena are not yet clear. For a MBL system in the presence of non-reciprocal tunnelings and random disorder potential, we identify two different complex-real spectral transitions, one is present for both open and periodic boundaries while the other is present only for open boundaries of a coupled non-Hermitian chains. The later is driven due to the inter-chain coupling at weak disorder where the level statistics of the real eigenenergy phase follows Gaussian orthogonal ensemble. We further characterize wavefunctions through the (biorthogonal) inverse participation ratio and fractal dimension, which reveal the suppression of skin effect in the non-Hermitian MBL phase. Finally, we demonstrate that the quench dynamics of the local particle density, spin imbalance, and entanglement entropy also signify the hallmark of the boundary effects and non-ergodic character of many-body localization.
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Submitted 23 August, 2022; v1 submitted 25 February, 2022;
originally announced February 2022.
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Quantum correlations of localized atomic excitations in a disordered atomic chain
Authors:
H. H. Jen
Abstract:
Atom-waveguide interface mediates significant and long-range light-matter interactions through the guided modes. In this one-dimensional system, we theoretically investigate the excitation localization of multiple atomic excitations under strong position disorders. Deep in the localization side, we obtain the time evolutions of quantum correlations via Kubo cumulant expansions, which arise initial…
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Atom-waveguide interface mediates significant and long-range light-matter interactions through the guided modes. In this one-dimensional system, we theoretically investigate the excitation localization of multiple atomic excitations under strong position disorders. Deep in the localization side, we obtain the time evolutions of quantum correlations via Kubo cumulant expansions, which arise initially and become finite and leveled afterward, overtaking the ones without disorders. This indicates two distinct regimes in time: before the onset of excitation localization, the disorders engage the disturbance of quantum correlations, which is followed by disorder-assisted build-up of quantum correlations that maintain at a later stage owing to the absence of excitations diffusion. The crossing of distinct regimes is pushed further in time for longer-range correlations, which indicates a characteristic timescale needed for disorders to sustain them. We also explore the effect of directionality of couplings and resonant dipole-dipole interactions, which can drive the system toward the delocalized side when it is under chiral couplings or large dipole-dipole interaction strengths. The time-evolved quantum correlations can give insights to the studies of few-body localization phenomenon and nonequilibrium dynamics in open quantum systems.
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Submitted 21 October, 2021;
originally announced October 2021.
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A non-Hermitian optical atomic mirror
Authors:
Yi-Cheng Wang,
Jhih-Shih You,
H. H. Jen
Abstract:
Explorations of symmetry and topology have led to important breakthroughs in quantum optics, but much richer behaviors arise from the non-Hermitian nature of light-matter interactions. A high-reflectivity, non-Hermitian optical mirror can be realized by a two-dimensional subwavelength array of neutral atoms near the cooperative resonance associated with the collective dipole modes. Here we show th…
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Explorations of symmetry and topology have led to important breakthroughs in quantum optics, but much richer behaviors arise from the non-Hermitian nature of light-matter interactions. A high-reflectivity, non-Hermitian optical mirror can be realized by a two-dimensional subwavelength array of neutral atoms near the cooperative resonance associated with the collective dipole modes. Here we show that exceptional points develop from a nondefective degeneracy by lowering the crystal symmetry of a square atomic lattice, and dispersive bulk Fermi arcs that originate from exceptional points are truncated by the light cone. We also find, although the dipole-dipole interaction is reciprocal, the geometry-dependent non-Hermitian skin effect emerges. Furthermore, skin modes localized at a boundary show a scale-free behavior that stems from the long-range interaction and whose mechanism goes beyond the framework of non-Bloch band theory. Our work opens the door to the study of the interplay among non-Hermiticity, topology, and long-range interaction.
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Submitted 24 December, 2021; v1 submitted 19 October, 2021;
originally announced October 2021.
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Bound and Subradiant Multi-Atom Excitations in an Atomic Array with Nonreciprocal Couplings
Authors:
H. H. Jen
Abstract:
Collective decays of multiply-excited atoms become subradiant and bound in space when they are strongly coupled to the guided modes in an atom-waveguide interface. In this interface, we analyze their average density-density and modified third-order correlations via Kubo cumulant expansions, which can arise and sustain for long time. The shape-preserving dimers and trimers of atomic excitations eme…
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Collective decays of multiply-excited atoms become subradiant and bound in space when they are strongly coupled to the guided modes in an atom-waveguide interface. In this interface, we analyze their average density-density and modified third-order correlations via Kubo cumulant expansions, which can arise and sustain for long time. The shape-preserving dimers and trimers of atomic excitations emerge in the most subradiant coupling regime of light-induced dipole-dipole interactions. This leads to a potential application of quantum information processing and quantum storage in the encoded nonreciprocal spin diffusion, where its diffusion speed depends on the initial coherence between the excited atoms and is robust to their relative phase fluctuations. The state-dependent photon routing can be viable as well in this interface.
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Submitted 7 February, 2021;
originally announced February 2021.
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Crossover from a delocalized to localized atomic excitation in an atom-waveguide interface
Authors:
H. H. Jen,
J. -S. You
Abstract:
An atom-waveguide system, which presents one of the quantum interfaces that enable strong couplings between light and atoms, can support tightly-confined guided modes of light. In this distinctive quantum interface, we theoretically investigate the crossover from a delocalized to localized atomic excitation under long-range dipole-dipole interactions and lattice disorders. Both localization length…
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An atom-waveguide system, which presents one of the quantum interfaces that enable strong couplings between light and atoms, can support tightly-confined guided modes of light. In this distinctive quantum interface, we theoretically investigate the crossover from a delocalized to localized atomic excitation under long-range dipole-dipole interactions and lattice disorders. Both localization lengths of the excitation distributions and power-law scalings of dissipative von Neumann entanglement entropy show signatures of this crossover. We further calculate numerically the level statistics of the underlying non-Hermitian Hamiltonian, from which as the disorder strength increases, the gap ratio decreases and the intrasample variance increases before reaching respective saturated values. The mean gap ratio in the deeply localized regime is close to the one from Poisson statistics along with a relatively large intrasample variance, whereas in the nondisordered regime, a significant level repulsion emerges. Our results provide insights to study the non-ergodic phenomenon in an atom-waveguide interface, which can be potentially applied to photon storage in this interface under dissipations.
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Submitted 31 December, 2020;
originally announced December 2020.
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Disorder-assisted excitation localization in chirally coupled quantum emitters
Authors:
H. H. Jen
Abstract:
One-dimensional quantum emitters with chiral couplings can exhibit nonreciprocal decay channels, along with light-induced dipole-dipole interactions mediated via an atom-waveguide interface. When the position disorders are introduced to such atomic array, we are able to identify the dynamical phase transition from excitation delocalization to localization, with an interplay between the directional…
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One-dimensional quantum emitters with chiral couplings can exhibit nonreciprocal decay channels, along with light-induced dipole-dipole interactions mediated via an atom-waveguide interface. When the position disorders are introduced to such atomic array, we are able to identify the dynamical phase transition from excitation delocalization to localization, with an interplay between the directionality of decay rates and the strength of light-induced dipole-dipole interactions. Deep in the localization phase, its characteristic length decreases and saturates toward a reciprocal coupling regime, leading to a system dynamics whose ergodicity is strongly broken. We also find an interaction-driven re-entrant behavior of the localization phase and a reduction of level repulsion under strong disorder. The former coincides with a drop in the exponent of power-law decaying von Neumann entropy, which gives insights to a close relation between the preservation of entanglement and nonequilibrium dynamics in open quantum systems, while the latter presents a distinct narrow distribution of gap ratios in this particular disordered system.
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Submitted 20 May, 2020;
originally announced May 2020.
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Steady-state Phase Diagram of a Weakly Driven Chiral-coupled Atomic Chain
Authors:
H. H. Jen
Abstract:
A chiral-coupled atomic chain of two-level quantum emitters allows strong resonant dipole-dipole interactions, which enables significant collective couplings between every other emitters. We numerically obtain the steady-state phase diagram of such system under weak excitations, where interaction-driven states of crystalline orders, edge or hole excitations, and dichotomy of chiral flow are identi…
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A chiral-coupled atomic chain of two-level quantum emitters allows strong resonant dipole-dipole interactions, which enables significant collective couplings between every other emitters. We numerically obtain the steady-state phase diagram of such system under weak excitations, where interaction-driven states of crystalline orders, edge or hole excitations, and dichotomy of chiral flow are identified. We distinguish these phases by participation ratios and structure factors, and find two critical points which relate to decoherence-free subradiant sectors of the system. We further investigate the transport of excitations and emergence of crystalline orders under spatially-varying excitation detunings, and present non-ergodic butterfly-like system dynamics in the phase of extended hole excitations with a signature of persistent subharmonic oscillations. Our results demonstrate the interaction-induced quantum phases of matter with chiral couplings, and pave the way toward simulations of many-body states in nonreciprocal quantum optical systems.
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Submitted 28 September, 2019;
originally announced September 2019.
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Subradiance dynamics in a singly-excited chiral-coupled atomic chain
Authors:
H. H. Jen,
M. -S. Chang,
G. -D. Lin,
Y. -C. Chen
Abstract:
We theoretically investigate the subradiance dynamics in a nonreciprocal chiral-coupled atomic chain, in which infinite-range dipole-dipole interaction emerges in the dissipation. We find that super- and subradiance are both present in the dissipation process following single photon excitation, and the decay dynamics shows burst emissions from uniform initial excitations, which reflects the influe…
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We theoretically investigate the subradiance dynamics in a nonreciprocal chiral-coupled atomic chain, in which infinite-range dipole-dipole interaction emerges in the dissipation. We find that super- and subradiance are both present in the dissipation process following single photon excitation, and the decay dynamics shows burst emissions from uniform initial excitations, which reflects the influence of atomic ordering on the propagation of light-induced atom-atom correlations. By tuning the nonreciprocal couplings in the chiral-coupled atomic system, we show that the subradiance dynamics can be greatly modified. We further study the effect of atomic local disorder, and find occurrence of plateaus on the decay curve dependent on the defect locations, as well as persistent localized excitations induced by disorders. We also discuss the effect of imperfections of systems on the subradiance dynamics. Our results show rich opportunities in the chiral-coupled system toward photon storage and routing.
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Submitted 29 January, 2020; v1 submitted 1 May, 2019;
originally announced May 2019.
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Quantum-coherence-enhanced subradiance in a chiral-coupled atomic chain
Authors:
H. H. Jen
Abstract:
We theoretically study the quantum-coherence-enhanced subradiance in a chiral-coupled atomic chain with nonreciprocal decay channels. The collective radiation in this one-dimensional (1D) nanophotonics system results from the resonant dipole-dipole interactions (RDDI) in 1D reservoirs, which allow infinite-range couplings between atoms. When single photon interacts with part of the atomic chain fr…
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We theoretically study the quantum-coherence-enhanced subradiance in a chiral-coupled atomic chain with nonreciprocal decay channels. The collective radiation in this one-dimensional (1D) nanophotonics system results from the resonant dipole-dipole interactions (RDDI) in 1D reservoirs, which allow infinite-range couplings between atoms. When single photon interacts with part of the atomic chain from a side excitation, the subradiant decay can be further reduced when highly correlated states are initially excited. The excitation plateau in the decay process can emerge due to the ordered population exchanges, which presents one distinctive signature of long-range and light-induced atom-atom correlations. Multiple time scales of the decay behaviors also show up due to multiple scattering of light transmissions and reflections in the chain. We further investigate the effect of atomic position fluctuations, and find that the cascaded scheme with uni-directional coupling is more resilient to the fluctuations, while the overall decay constant can be increased due to large deviations. Our results present a fundamental study on the subradiance and light-induced atom-atom correlations in such 1D nanophotonics platforms, and offer rich opportunities in potential applications of quantum storage of photons.
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Submitted 9 April, 2020; v1 submitted 13 March, 2019;
originally announced March 2019.
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Selective transport of atomic excitations in a driven chiral-coupled atomic chain
Authors:
H. H. Jen
Abstract:
We theoretically investigate the flow of the atomic excitations in a driven chiral-coupled atomic chain with nonreciprocal decay channels. This one-dimensional system allows infinite-range dipole-dipole interaction, and enables directional guided modes of scattered light. Under a weakly driven condition, we are able to simulate the transport properties of atomic excitations between the left and ri…
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We theoretically investigate the flow of the atomic excitations in a driven chiral-coupled atomic chain with nonreciprocal decay channels. This one-dimensional system allows infinite-range dipole-dipole interaction, and enables directional guided modes of scattered light. Under a weakly driven condition, we are able to simulate the transport properties of atomic excitations between the left and right parts of the chain. In the steady states, the transport is highly dependent on the equidistant positions of the ordered array, the excitation field detunings, and the directionality of such chiral-coupled system. We discuss the parameter regimes which are resilient or sensitive to position fluctuations, and provide insights to precise and genuine state preparations. Furthermore, we study the effect of position fluctuations on the transport of excitations. Our results can shed light on deterministic state preparations and pave the way for many-body state manipulations in the driven and dissipative chiral-coupled systems.
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Submitted 29 November, 2018;
originally announced November 2018.
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Super- and Sub-radiance from Two-dimensional Resonant Dipole-dipole Interactions
Authors:
H. H. Jen
Abstract:
We theoretically investigate the super- and sub-radiance from the resonant dipole-dipole interactions (RDDI) in a confined two-dimensional (2D) reservoir. The distinctive feature of 2D RDDI shows qualitatively and quantitatively different long-range behavior from RDDI in free space. We investigate the superradiant properties of the singly-excited symmetric state under this 2D RDDI. This state also…
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We theoretically investigate the super- and sub-radiance from the resonant dipole-dipole interactions (RDDI) in a confined two-dimensional (2D) reservoir. The distinctive feature of 2D RDDI shows qualitatively and quantitatively different long-range behavior from RDDI in free space. We investigate the superradiant properties of the singly-excited symmetric state under this 2D RDDI. This state also allows subradiant decays in much longer distances than the transition wavelength, showing long-range atom-atom correlations. We further study the dynamics of the subradiant states which can be accessed by imprinting spatially dependent phases on the atomic arrays. Our results demonstrate rich opportunities in engineering light-matter interactions in a confined 2D reservoir, and hold promise in applications of quantum light storage and single-excitation state manipulations.
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Submitted 29 January, 2019; v1 submitted 22 October, 2018;
originally announced October 2018.
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Spin-incoherent Luttinger liquid of one-dimensional SU($κ$) fermions
Authors:
H. H. Jen,
S. -K. Yip
Abstract:
We theoretically investigate one-dimensional (1D) SU($κ$) fermions in the regime of spin-incoherent Luttinger liquid. We specifically focus on the Tonks-Girardeau gas limit where its density is sufficiently low that effective repulsions between atoms become infinite. In such case, spin exchange energy of 1D SU($κ$) fermions vanishes and all spin configurations are degenerate, which automatically p…
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We theoretically investigate one-dimensional (1D) SU($κ$) fermions in the regime of spin-incoherent Luttinger liquid. We specifically focus on the Tonks-Girardeau gas limit where its density is sufficiently low that effective repulsions between atoms become infinite. In such case, spin exchange energy of 1D SU($κ$) fermions vanishes and all spin configurations are degenerate, which automatically puts them into spin-incoherent regime. In this limit, we are able to express the single-particle density matrices in terms of those of anyons. This allows us to numerically simulate the number of particles up to $N=32$. We numerically calculate single-particle density matrices in two cases: (1) equal populations for each spin components (balanced) and (2) all $S_z$ manifolds included. In contrast to noninteracting multi-component fermions, the momentum distributions are broadened due to strong interactions. As $κ$ increases, the momentum distributions are less broadened for fixed $N$, while they are more broadened for fixed number of particle per spin component. We then compare numerically calculated high momentum tails with analytical predictions which are proportional to $1/p^4$, in good agreement. Thus, our theoretical study provides a comparison with the experiments of repulsive multicomponent alkaline-earth fermions with a tunable SU($κ$) spin-symmetry in the spin-incoherent regime.
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Submitted 7 May, 2018;
originally announced May 2018.
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Directional subradiance from helical-phase-imprinted multiphoton states
Authors:
H. H. Jen
Abstract:
We theoretically investigate the far-field scattering properties of multiphoton super- and subradiant states which can be prepared by multiphoton excitations with orbital angular momentum (OAM).\ Due to multiphoton interference, the far-field patterns of the subradiant modes show directional scattering along the excitation direction or transverse scattering with number of peaks equal to the number…
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We theoretically investigate the far-field scattering properties of multiphoton super- and subradiant states which can be prepared by multiphoton excitations with orbital angular momentum (OAM).\ Due to multiphoton interference, the far-field patterns of the subradiant modes show directional scattering along the excitation direction or transverse scattering with number of peaks equal to the number of atoms.\ When more atoms are involved, we consider structures of stacked and concentric rings, which respectively show enhanced directional scattering and smoothed emission patterns.\ Our scheme gives insights to prepare many-body subradiant states, and is potentially applicable to quantum storage of multiphoton with OAM.\ By designing atomic spatial distributions, these cooperative states can tailor the far-field emission properties, which is useful for light collections and quantum information manipulations.
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Submitted 9 January, 2018;
originally announced January 2018.
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Cooperative light scattering from helical-phase-imprinted atomic rings
Authors:
H. H. Jen,
M. -S. Chang,
Y. -C. Chen
Abstract:
We theoretically investigate the light scattering of the super- and subradiant states which can be prepared by the excitation of a single photon which carries an orbital angular momentum (OAM).\ With this helical phase imprinted on the stacked ring of atomic arrays, the subradiant modes show directional side scattering in the far-field, allowing for light collimation and quantum storage of light w…
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We theoretically investigate the light scattering of the super- and subradiant states which can be prepared by the excitation of a single photon which carries an orbital angular momentum (OAM).\ With this helical phase imprinted on the stacked ring of atomic arrays, the subradiant modes show directional side scattering in the far-field, allowing for light collimation and quantum storage of light with OAM.\ For the excitations with linear polarizations, we find a discrete $C_4$ rotational symmetry in scattering for the number of atoms $N$ $=$ $4n $ with integers $n$, while for circular polarizations with arbitrary $N$, the azimuthal and $C_N$ symmetries emerge for the super- and subradiant modes respectively.\ When the radial and azimuthal polarizations are considered, a mode shift can happen in the scattering pattern.\ The forward scattering of the superradiant modes can be enhanced as we stack up the rings along the excitation direction, and for the subradiant modes, we find the narrowing effects on the scattering in the azimuthal and the polar angles when more concentric rings are added in the radial direction.\ By designing the atomic spatial distributions and excitation polarizations, helical-phase-imprinted subradiant states can tailor and modify the radiation properties, which is detectable in the directional super- and subradiant emissions and is potentially useful in quantum information manipulations.
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Submitted 2 January, 2018;
originally announced January 2018.
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Spin-incoherent Luttinger liquid of one-dimensional spin-1 Tonks-Girardeau Bose gas: Spin-dependent properties
Authors:
H. H. Jen,
S. -K. Yip
Abstract:
Spin-incoherent Luttinger liquid (SILL) is a different universal class from the Luttinger liquid.\ This difference results from the spin incoherence of the system when the thermal energy of the system is higher than the spin excitation energy.\ We consider one-dimensional spin-$1$ Bose gas in the SILL regime and investigate its spin-dependent many-body properties.\ In Tonks-Girardeau limit, we are…
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Spin-incoherent Luttinger liquid (SILL) is a different universal class from the Luttinger liquid.\ This difference results from the spin incoherence of the system when the thermal energy of the system is higher than the spin excitation energy.\ We consider one-dimensional spin-$1$ Bose gas in the SILL regime and investigate its spin-dependent many-body properties.\ In Tonks-Girardeau limit, we are able to write down the general wave functions in a harmonic trap.\ We numerically calculate the spin-dependent (spin-plus, minus, and $0$) momentum distributions in the sector of zero magnetization which allows to demonstrate the most significant spin-incoherent feature compared to the spinless or spin-polarized case.\ In contrast to the spinless Bose gas, the momentum distributions are broadened and in the large momentum limit follow the same asymptotic $1/p^4$ dependence but with reduced coefficients.\ While the density matrices and momentum distributions differ between different spin components for small $N$, at large $N$ they approach each other.\ We show these by analytic arguments and numerical calculations up to $N$ $=$ $16$.
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Submitted 27 March, 2017;
originally announced March 2017.
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Spin-incoherent one-dimensional spin-1 Bose Luttinger liquid
Authors:
H. H. Jen,
S. -K. Yip
Abstract:
We investigate spin-incoherent Luttinger liquid of a one-dimensional spin-1 Bose gas in a harmonic trap. In this regime highly degenerate spin configurations emerge since the spin exchange energy is much less than the thermal energy of the system, while the temperature is low enough that the lowest energetic orbitals are occupied. As an example we numerically study the momentum distribution of a o…
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We investigate spin-incoherent Luttinger liquid of a one-dimensional spin-1 Bose gas in a harmonic trap. In this regime highly degenerate spin configurations emerge since the spin exchange energy is much less than the thermal energy of the system, while the temperature is low enough that the lowest energetic orbitals are occupied. As an example we numerically study the momentum distribution of a one-dimensional spin-1 Bose gas in Tonks- Girardeau gas limit and in the sector of zero magnetization.We find that the momentum distributions broaden as the number of atoms increase due to the averaging of spin function overlaps. Large momentum ($p$) asymptotic is analytically derived, showing the universal $1/p^4$ dependence. We demonstrate that the spin-incoherent Luttinger liquid has a momentum distribution also distinct from spinless bosons at finite temperature.
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Submitted 30 June, 2016; v1 submitted 2 May, 2016;
originally announced May 2016.
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Fragmented Many-body States of Spin-2 Bose Gas
Authors:
H. H. Jen,
S. -K. Yip
Abstract:
We investigate the fragmented many-body ground states of a spin-2 Bose gas in zero magnetic field.\ We point out that the exact ground state is not simply an average over rotationally-invariant mean-field states, in contrast to the spin-1 case with even number of particles N.\ We construct the exact ground states and compare them with the angular-averaged polar and cyclic states.\ The angular-aver…
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We investigate the fragmented many-body ground states of a spin-2 Bose gas in zero magnetic field.\ We point out that the exact ground state is not simply an average over rotationally-invariant mean-field states, in contrast to the spin-1 case with even number of particles N.\ We construct the exact ground states and compare them with the angular-averaged polar and cyclic states.\ The angular-averaged polar states fail to retrieve the exact eigenstate at $N$ $\ge$ $6$ while angular-averaged cyclic states sustain only for N with a multiple of $3$.\ We calculate the density matrices and two-particle density matrices to show how deviant the angular-averaged state is from the exact one.
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Submitted 16 April, 2015; v1 submitted 16 February, 2015;
originally announced February 2015.
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Extracting Dynamical Green's Function of Ultracold Quantum Gases via Electromagnetically Induced Transparency
Authors:
H. H. Jen,
Daw-Wei Wang
Abstract:
The essential quantum many-body physics of an ultracold quantum gas relies on the single-particle Green's functions.\ We demonstrate that it can be extracted by the spectrum of electromagnetically induced transparency (EIT).\ The single-particle Green's function can be reconstructed by the measurements of frequency moments in EIT spectroscopy.\ This optical measurement provides an efficient and no…
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The essential quantum many-body physics of an ultracold quantum gas relies on the single-particle Green's functions.\ We demonstrate that it can be extracted by the spectrum of electromagnetically induced transparency (EIT).\ The single-particle Green's function can be reconstructed by the measurements of frequency moments in EIT spectroscopy.\ This optical measurement provides an efficient and nondestructive method to reveal the many-body properties, and we propose an experimental setup to realize it.\ Finite temperature and finite size effects are discussed, and we demonstrate the reconstruction steps of Green's function for the examples of three-dimensional Mott-insulator phase and one-dimensional Luttinger liquid.
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Submitted 30 October, 2014; v1 submitted 9 March, 2014;
originally announced March 2014.
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P-wave Superfluidity by Blockade Effects in a Rydberg-Dressed Fermi Gas
Authors:
Bo Xiong,
H. H. Jen,
Daw-Wei Wang
Abstract:
We systematically investigate the p-wave superfluidity of a Rydberg-dressed Fermi gas, where the soft-core effective interaction is of finite radius $R_{c}$ due to blockade effects. After solving the BCS gap equation and comparing the free energy, we obtain the quantum phase diagram, which is composed of three different phases: polar ($p_{z}$), axial ($p_{x}+ip_{y}$), and axi-planar (…
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We systematically investigate the p-wave superfluidity of a Rydberg-dressed Fermi gas, where the soft-core effective interaction is of finite radius $R_{c}$ due to blockade effects. After solving the BCS gap equation and comparing the free energy, we obtain the quantum phase diagram, which is composed of three different phases: polar ($p_{z}$), axial ($p_{x}+ip_{y}$), and axi-planar ($p_{x}+iβ_{p}p_{y}$) phases. The tri-critical point locates around $R_{c}k_{F}\sim1$, where $k_{F}$ is the Fermi wave vector. We further derive the Ginzburg-Landau theory to explain the phase diagram, and estimate the transition temperature to be about 0.1$E_{F}$ in the current experimental regime of $^{6}$Li. Our work paves the way for future studies on p-wave superfluids and related quantum phase transitions in ultracold atoms.
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Submitted 3 August, 2013; v1 submitted 20 July, 2013;
originally announced July 2013.
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Theory of Electromagnetically Induced Transparency in Strongly Correlated Quantum Gases
Authors:
H. H. Jen,
Daw-Wei Wang
Abstract:
We develop a general theory to study the electromagnetically induced transparency (EIT) in ultracold quantum gases, applicable for both Bose and Fermi gases with arbitrary inter-particle interaction strength. We show that, in the weak probe field limit, the EIT spectrum is solely determined by the single particle Green's function of the ground state atoms, and reflects interesting quantum many-bod…
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We develop a general theory to study the electromagnetically induced transparency (EIT) in ultracold quantum gases, applicable for both Bose and Fermi gases with arbitrary inter-particle interaction strength. We show that, in the weak probe field limit, the EIT spectrum is solely determined by the single particle Green's function of the ground state atoms, and reflects interesting quantum many-body effects when atoms are virtually coupled to the low-lying Rydberg states. As an example, we apply our theory to 1D Luttinger liquid, Bose-Mott insulator state, and the superfluid state of two-component Fermi gases, and show how the many-body features can be observed non-destructively in the unconventional EIT spectrum.
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Submitted 14 June, 2013; v1 submitted 14 March, 2013;
originally announced March 2013.
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Electromagnetic induced transparency and slow light in interacting quantum degenerate atomic gases
Authors:
H. H. Jen,
Bo Xiong,
Ite A. Yu,
Daw-Wei Wang
Abstract:
We systematically develop the full quantum theory for the electromagnetic induced transparency (EIT) and slow light properties in ultracold Bose and Fermi gases. It shows a very different property from the classical theory which assumes frozen atomic motion. For example, the speed of light inside the atomic gases can be changed dramatically near the Bose-Einstein condensation temperature, while th…
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We systematically develop the full quantum theory for the electromagnetic induced transparency (EIT) and slow light properties in ultracold Bose and Fermi gases. It shows a very different property from the classical theory which assumes frozen atomic motion. For example, the speed of light inside the atomic gases can be changed dramatically near the Bose-Einstein condensation temperature, while the presence of the Fermi sea can destroy the EIT effect even at zero temperature. From experimental point of view, such quantum EIT property is mostly manifested in the counter-propagating excitation schemes in either the low-lying Rydberg transition with a narrow line width or in the D2 transitions with a very weak coupling field. We further investigate the interaction effects on the EIT for a weakly interacting Bose-Einstein condensate, showing an inhomogeneous broadening of the EIT profile and nontrivial change of the light speed due to the quantum many-body effects beyond mean field energy shifts.
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Submitted 13 December, 2012; v1 submitted 1 August, 2012;
originally announced August 2012.
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The angular momentum of a magnetically trapped atomic condensate
Authors:
P. Zhang,
H. H. Jen,
C. P. Sun,
L. You
Abstract:
For an atomic condensate in an axially symmetric magnetic trap, the sum of the axial components of the orbital angular momentum and the hyperfine spin is conserved. Inside an Ioffe-Pritchard trap (IPT) whose magnetic field (B-field) is not axially symmetric, the difference of the two becomes surprisingly conserved. In this paper we investigate the relationship between the values of the sum/diffe…
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For an atomic condensate in an axially symmetric magnetic trap, the sum of the axial components of the orbital angular momentum and the hyperfine spin is conserved. Inside an Ioffe-Pritchard trap (IPT) whose magnetic field (B-field) is not axially symmetric, the difference of the two becomes surprisingly conserved. In this paper we investigate the relationship between the values of the sum/difference angular momentums for an atomic condensate inside a magnetic trap and the associated gauge potential induced by the adiabatic approximation. Our result provides significant new insight into the vorticity of magnetically trapped atomic quantum gases.
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Submitted 19 January, 2007; v1 submitted 14 November, 2006;
originally announced November 2006.