Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1607.06923 · Physical Review A

Vortex formation and dynamics in two-dimensional driven-dissipative condensates

F. Hebenstreit

Published Dec 16, 2016• 4 citations
arXivHTMLPDF

Abstract

We investigate the real-time evolution of lattice bosons in two spatial dimensions whose dynamics is governed by a Markovian quantum master equation. We employ the Wigner-Weyl phase space quantization and derive the functional integral for open quantum many-body systems that determines the time evolution of the Wigner function. Using the truncated Wigner approximation, in which quantum fluctuations are only taken into account in the initial state whereas the dynamics is governed by classical evolution equations, we study the buildup of long-range correlations due to the action of non-Hermitean quantum jump operators that constitute a mechanism for dissipative cooling. Starting from an initially disordered state corresponding to a vortex condensate, the dissipative process results in the annihilation of vortex-antivortex pairs and the establishment of quasi-long-range order at late times. We observe that a finite vortex density survives the cooling process, which disagrees with the analytically constructed vortex-free Bose-Einstein condensate at asymptotic times. This indicates that quantum fluctuations beyond the truncated Wigner approximation need to be included to fully capture the physics of dissipative Bose-Einstein condensation.

DOI
10.1103/physreva.94.063617

Related papers

Dissipative Bose–Einstein condensation in contact with a thermal reservoir

S Caspar, F Hebenstreit, D Mesterházy +1 more

We investigate the real-time dynamics of open quantum spin-1/2 or hardcore boson systems on a spatial lattice, which are governed by a Markovian quantum master equation. We derive general conditions under which the hierarchy of correlation functions closes such that their time evolution can be computed semi-analytically. Expanding our previous work (2016 Phys. Rev. A 93 021602 ) we demonstrate the universality of a purely dissipative quantum Markov process that drives the system of spin-1/2 particles into a totally symmetric superposition state, corresponding to a Bose–Einstein condensate of hardcore bosons. In particular, we show that the finite-size scaling behavior of the dissipative gap is independent of the chosen boundary conditions and the underlying lattice structure. In addition, we consider the effect of a uniform magnetic field as well as a coupling to a thermal bath to investigate the susceptibility of the engineered dissipative process to unitary and nonunitary perturbations. We establish the nonequilibrium steady-state phase diagram as a function of temperature and dissipative coupling strength. For a small number of particles N , we identify a parameter region in which the engineered symmetrizing dissipative process performs robustly, while in the thermodynamic limit N → ∞ , the coupling to the thermal bath destroys any long-range order.

arXiv:1604.03725•New Journal of Physics•Jul 7, 2016•11 citations

Systematic Truncated Wigner Approximation for Open Spin Systems Reveals Long-Range Order Far from Equilibrium

Igor Timofeev, Dawid A. Hryniuk, Marzena H. Szymańska

Long-range interactions can protect dissipative order against fluctuations, but determining when they do so in two dimensions remains out of reach for existing many-body methods. We develop a continuous SU(2)-covariant truncated-Wigner framework that maps the problem onto stochastic dynamics with one Bloch sphere per site. Derived systematically from the exact Stratonovich-Weyl evolution of the Lindblad equation, it generates both drift and reservoir noise for arbitrary spin $S$. Benchmarks against exact and tensor-network calculations validate its description of non-equilibrium dynamics and steady states. Applied to 400-site two-dimensional dissipative anisotropic XY lattices, our method reveals physics missed by mean-field and perturbative approaches: vortex-antivortex proliferation destroys the predicted staggered-XY phase for nearest-neighbour coupling, whereas algebraically decaying interactions stabilize an extended $\mathbb{Z}_2$-ordered phase. We obtain the first beyond-mean-field steady-state phase diagram of the long-range interacting model, revealing reentrant loss of order at strong coupling and closure of the ordered region beyond $α\approx 3.5$. Our new method provides a scalable route to strongly correlated driven-dissipative systems with long-range interactions, higher-dimensional geometries, spin-boson couplings, and spins beyond one half, relevant to modern experiments with magnetic atoms and polar molecules in optical lattices and tweezer arrays.

quant-pharXiv:2610.27462•Oct 21, 2026•0 citations

Dissipative Bose–Einstein condensation in contact with a thermal reservoir

Caspar, Stephan, Hebenstreit, Florian, Mesterhazy, David +1 more

We investigate the real-time dynamics of open quantum spin-1/2 or hardcore boson systems on a spatial lattice, which are governed by a Markovian quantum master equation.Wederive general conditions under which the hierarchy of correlation functions closes such that their time evolution can be computed semi-analytically. Expanding our previous work (2016 Phys. Rev. A 93 021602) we demonstrate the universality of a purely dissipative quantum Markov process that drives the system of spin-1/2 particles into a totally symmetric superposition state, corresponding to a Bose–Einstein condensate of hardcore bosons. In particular, we show that the finite-size scaling behavior of the dissipative gap is independent of the chosen boundary conditions and the underlying lattice structure. In addition, we consider the effect of a uniform magnetic field as well as a coupling to a thermal bath to investigate the susceptibility of the engineered dissipative process to unitary and nonunitary perturbations.Weestablish the nonequilibrium steady-state phase diagram as a function of temperature and dissipative coupling strength. For a small number of particles N,we identify a parameter region in which the engineered symmetrizing dissipative process performs robustly, while in the thermodynamic limit N→∞, the coupling to the thermal bath destroys any long-range order.

•Jul 7, 2016•9 citations

Discrete-phase-space method for driven-dissipative dynamics of strongly interacting bosons in optical lattices

Kazuma Nagao, Ippei Danshita, Seiji Yunoki

We develop a discrete truncated Wigner method to analyze the real-time evolution of dissipative $\mathrm{SU}(\mathcal{N})$ spin systems coupled with a Markovian environment. This semiclassical approach is not only numerically efficient but also particularly capable of accurately capturing local loss processes due to its local linearity in the dynamical equations. We apply the method to a state-of-the-art experiment involving an analog quantum simulator of a three-dimensional dissipative Bose-Hubbard model in a strongly interacting regime. Our numerical results show good agreement with experimental data, specifically capturing the continuous quantum Zeno effect in the dynamics subjected to a gradual change of the ratio between the hopping amplitude and the onsite interaction across the superfluid Mott insulator crossover. Furthermore, we present comparative analyses with the continuous truncated Wigner method, derived as an effective Fokker-Planck equation for $\mathrm{SU}(\mathcal{N})$ classical spin variables, showing that the discrete method outperforms the continuous one in simulating the long-time dynamics of SU(2) and SU(3) spin models. The discrete phase-space framework offers a versatile and powerful tool for exploring a wide range of open quantum many-body systems in dimensions higher than one dimension, where numerically exact methods are impractical due to the exponential growth of the Hilbert-space dimension.

arXiv:2307.16170•Physical Review A•Dec 11, 2024•5 citations

Dynamical Transition of Quantum Vortex-Pair Annihilation in a Bose-Einstein Condensate

Toshiaki Kanai, Chuanwei Zhang

Understanding the elementary mechanism for the dissipation of vortex energy in quantum liquids is one central issue in quantum hydrodynamics, such as quantum turbulence in systems ranging from neutron stars to atomic condensates. In a two-dimensional (2D) Bose-Einstein condensate (BEC) at zero temperature, besides the vortex drift-out process from the boundary, vortex-antivortex pair can annihilate in the bulk, but controversy remains on the number of vortices involved in the annihilation process. We find there exists a dynamical transition from four-body to three-body vortex annihilation processes with the time evolution in a boundary-less uniform quasi-2D BEC. Such dynamical transition depends on the initial vortex pair density, and occurs when the sound waves generated in the vortex annihilation process surpass a critical energy. With the confinement along the third direction is relaxed in a quasi-2D BEC, the critical sound wave energy decreases due to the 3D vortex line curve and reconnection, shifting the dynamical transition to the early time. Our work reveals an elementary mechanism for the dissipation of vortex energy that may help understand exotic matter and dynamics in quantum liquids.

arXiv:2407.14627•Jul 19, 2024•0 citations

Dynamical crossover of vortex-pair annihilation in two-dimensional quantum turbulence

Toshiaki Kanai, Chuanwei Zhang

Understanding the elementary mechanism for the dissipation of vortex energy in quantum liquids is one central issue in quantum hydrodynamics, such as quantum turbulence in systems ranging from neutron stars to atomic condensates. In a two-dimensional (2D) Bose-Einstein condensate (BEC) at zero temperature, in addition to the vortex drift-out process from the boundary, a vortex-antivortex pair can annihilate in bulk, but controversy remains on the number of vortices involved in the annihilation process. We find that a dynamic crossover exists from four-body to three-body vortex annihilation processes with time evolution in decaying 2D quantum turbulence of a boundary-less uniform quasi-2D BEC. Such a dynamical crossover depends on the initial vortex pair density and occurs when the sound waves generated in the vortex annihilation process surpass a threshold energy. As the confinement along the third direction is relaxed in a quasi-2D BEC, the threshold sound wave energy decreases due to the three-dimensional (3D) vortex line curve and reconnection, shifting the dynamical crossover to the early time. Our work reveals an elementary mechanism for the dissipation of vortex energy that may help understand exotic matter and dynamics in quantum liquids.

Physical Review A•Aug 11, 2025•2 citations
We investigate the real-time evolution of lattice bosons in two spatial dimensions whose dynamics is governed by a Markovian quantum master equation. We employ the Wigner-Weyl phase space quantization and derive the functional integral for open quantum many-body systems that determines the time evolution of the Wigner function. Using the truncated Wigner approximation, in which quantum fluctuations are only taken into account in the initial state whereas the dynamics is governed by classical evolution equations, we study the buildup of long-range correlations due to the action of non-Hermitean quantum jump operators that constitute a mechanism for dissipative cooling. Starting from an initially disordered state corresponding to a vortex condensate, the dissipative process results in the annihilation of vortex-antivortex pairs and the establishment of quasi-long-range order at late times. We observe that a finite vortex density survives the cooling process, which disagrees with the analytically constructed vortex-free Bose-Einstein condensate at asymptotic times. This indicates that quantum fluctuations beyond the truncated Wigner approximation need to be included to fully capture the physics of dissipative Bose-Einstein condensation.
We investigate the real-time dynamics of open quantum spin-1/2 or hardcore boson systems on a spatial lattice, which are governed by a Markovian quantum master equation. We derive general conditions under which the hierarchy of correlation functions closes such that their time evolution can be computed semi-analytically. Expanding our previous work (2016 Phys. Rev. A 93 021602 ) we demonstrate the universality of a purely dissipative quantum Markov process that drives the system of spin-1/2 particles into a totally symmetric superposition state, corresponding to a Bose–Einstein condensate of hardcore bosons. In particular, we show that the finite-size scaling behavior of the dissipative gap is independent of the chosen boundary conditions and the underlying lattice structure. In addition, we consider the effect of a uniform magnetic field as well as a coupling to a thermal bath to investigate the susceptibility of the engineered dissipative process to unitary and nonunitary perturbations. We establish the nonequilibrium steady-state phase diagram as a function of temperature and dissipative coupling strength. For a small number of particles N , we identify a parameter region in which the engineered symmetrizing dissipative process performs robustly, while in the thermodynamic limit N → ∞ , the coupling to the thermal bath destroys any long-range order.
Long-range interactions can protect dissipative order against fluctuations, but determining when they do so in two dimensions remains out of reach for existing many-body methods. We develop a continuous SU(2)-covariant truncated-Wigner framework that maps the problem onto stochastic dynamics with one Bloch sphere per site. Derived systematically from the exact Stratonovich-Weyl evolution of the Lindblad equation, it generates both drift and reservoir noise for arbitrary spin SSS. Benchmarks against exact and tensor-network calculations validate its description of non-equilibrium dynamics and steady states. Applied to 400-site two-dimensional dissipative anisotropic XY lattices, our method reveals physics missed by mean-field and perturbative approaches: vortex-antivortex proliferation destroys the predicted staggered-XY phase for nearest-neighbour coupling, whereas algebraically decaying interactions stabilize an extended Z2\mathbb{Z}_2Z2​-ordered phase. We obtain the first beyond-mean-field steady-state phase diagram of the long-range interacting model, revealing reentrant loss of order at strong coupling and closure of the ordered region beyond α≈3.5α\approx 3.5α≈3.5. Our new method provides a scalable route to strongly correlated driven-dissipative systems with long-range interactions, higher-dimensional geometries, spin-boson couplings, and spins beyond one half, relevant to modern experiments with magnetic atoms and polar molecules in optical lattices and tweezer arrays.
We investigate the real-time dynamics of open quantum spin-1/2 or hardcore boson systems on a spatial lattice, which are governed by a Markovian quantum master equation.Wederive general conditions under which the hierarchy of correlation functions closes such that their time evolution can be computed semi-analytically. Expanding our previous work (2016 Phys. Rev. A 93 021602) we demonstrate the universality of a purely dissipative quantum Markov process that drives the system of spin-1/2 particles into a totally symmetric superposition state, corresponding to a Bose–Einstein condensate of hardcore bosons. In particular, we show that the finite-size scaling behavior of the dissipative gap is independent of the chosen boundary conditions and the underlying lattice structure. In addition, we consider the effect of a uniform magnetic field as well as a coupling to a thermal bath to investigate the susceptibility of the engineered dissipative process to unitary and nonunitary perturbations.Weestablish the nonequilibrium steady-state phase diagram as a function of temperature and dissipative coupling strength. For a small number of particles N,we identify a parameter region in which the engineered symmetrizing dissipative process performs robustly, while in the thermodynamic limit N→∞, the coupling to the thermal bath destroys any long-range order.
We develop a discrete truncated Wigner method to analyze the real-time evolution of dissipative SU(N)\mathrm{SU}(\mathcal{N})SU(N) spin systems coupled with a Markovian environment. This semiclassical approach is not only numerically efficient but also particularly capable of accurately capturing local loss processes due to its local linearity in the dynamical equations. We apply the method to a state-of-the-art experiment involving an analog quantum simulator of a three-dimensional dissipative Bose-Hubbard model in a strongly interacting regime. Our numerical results show good agreement with experimental data, specifically capturing the continuous quantum Zeno effect in the dynamics subjected to a gradual change of the ratio between the hopping amplitude and the onsite interaction across the superfluid Mott insulator crossover. Furthermore, we present comparative analyses with the continuous truncated Wigner method, derived as an effective Fokker-Planck equation for SU(N)\mathrm{SU}(\mathcal{N})SU(N) classical spin variables, showing that the discrete method outperforms the continuous one in simulating the long-time dynamics of SU(2) and SU(3) spin models. The discrete phase-space framework offers a versatile and powerful tool for exploring a wide range of open quantum many-body systems in dimensions higher than one dimension, where numerically exact methods are impractical due to the exponential growth of the Hilbert-space dimension.
Understanding the elementary mechanism for the dissipation of vortex energy in quantum liquids is one central issue in quantum hydrodynamics, such as quantum turbulence in systems ranging from neutron stars to atomic condensates. In a two-dimensional (2D) Bose-Einstein condensate (BEC) at zero temperature, besides the vortex drift-out process from the boundary, vortex-antivortex pair can annihilate in the bulk, but controversy remains on the number of vortices involved in the annihilation process. We find there exists a dynamical transition from four-body to three-body vortex annihilation processes with the time evolution in a boundary-less uniform quasi-2D BEC. Such dynamical transition depends on the initial vortex pair density, and occurs when the sound waves generated in the vortex annihilation process surpass a critical energy. With the confinement along the third direction is relaxed in a quasi-2D BEC, the critical sound wave energy decreases due to the 3D vortex line curve and reconnection, shifting the dynamical transition to the early time. Our work reveals an elementary mechanism for the dissipation of vortex energy that may help understand exotic matter and dynamics in quantum liquids.
Understanding the elementary mechanism for the dissipation of vortex energy in quantum liquids is one central issue in quantum hydrodynamics, such as quantum turbulence in systems ranging from neutron stars to atomic condensates. In a two-dimensional (2D) Bose-Einstein condensate (BEC) at zero temperature, in addition to the vortex drift-out process from the boundary, a vortex-antivortex pair can annihilate in bulk, but controversy remains on the number of vortices involved in the annihilation process. We find that a dynamic crossover exists from four-body to three-body vortex annihilation processes with time evolution in decaying 2D quantum turbulence of a boundary-less uniform quasi-2D BEC. Such a dynamical crossover depends on the initial vortex pair density and occurs when the sound waves generated in the vortex annihilation process surpass a threshold energy. As the confinement along the third direction is relaxed in a quasi-2D BEC, the threshold sound wave energy decreases due to the three-dimensional (3D) vortex line curve and reconnection, shifting the dynamical crossover to the early time. Our work reveals an elementary mechanism for the dissipation of vortex energy that may help understand exotic matter and dynamics in quantum liquids.