1
|
Martirosyan G, Ho CJ, Etrych J, Zhang Y, Cao A, Hadzibabic Z, Eigen C. Observation of Subdiffusive Dynamic Scaling in a Driven and Disordered Bose Gas. PHYSICAL REVIEW LETTERS 2024; 132:113401. [PMID: 38563934 DOI: 10.1103/physrevlett.132.113401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2023] [Accepted: 01/05/2024] [Indexed: 04/04/2024]
Abstract
We explore the dynamics of a tuneable box-trapped Bose gas under strong periodic forcing in the presence of weak disorder. In absence of interparticle interactions, the interplay of the drive and disorder results in an isotropic nonthermal momentum distribution that shows subdiffusive dynamic scaling, with sublinear energy growth and the universal scaling function captured well by a compressed exponential. We explain that this subdiffusion in momentum space can naturally be understood as a random walk in energy space. We also experimentally show that for increasing interaction strength, the gas behavior smoothly crosses over to wave turbulence characterized by a power-law momentum distribution, which opens new possibilities for systematic studies of the interplay of disorder and interactions in driven quantum systems.
Collapse
Affiliation(s)
- Gevorg Martirosyan
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Christopher J Ho
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Jiří Etrych
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Yansheng Zhang
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Alec Cao
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Zoran Hadzibabic
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Christoph Eigen
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| |
Collapse
|
2
|
Begg SE, Davis MJ, Reeves MT. Nonequilibrium Transport in a Superfluid Josephson Junction Chain: Is There Negative Differential Conductivity? PHYSICAL REVIEW LETTERS 2024; 132:103402. [PMID: 38518323 DOI: 10.1103/physrevlett.132.103402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2023] [Revised: 12/10/2023] [Accepted: 02/06/2024] [Indexed: 03/24/2024]
Abstract
We consider the far-from-equilibrium quantum transport dynamics in a 1D Josephson junction chain of multimode Bose-Einstein condensates. We develop a theoretical model to examine the experiment of Labouvie et al. [Phys. Rev. Lett. 115, 050601 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.050601], wherein the phenomenon of negative differential conductivity (NDC) was reported in the refilling dynamics of an initially depleted site within the chain. We demonstrate that a unitary c-field description can quantitatively reproduce the experimental results over the full range of tunnel couplings, and requires no fitted parameters. With a view toward atomtronic implementations, we further demonstrate that the filling is strongly dependent on spatial phase variations stemming from quantum fluctuations. Our findings suggest that the interpretation of the device in terms of NDC is invalid outside of the weak coupling regime. Within this restricted regime, the device exhibits a hybrid behavior of NDC and the ac Josephson effect. A simplified circuit model of the device will require an approach tailored to atomtronics that incorporates quantum fluctuations.
Collapse
Affiliation(s)
- Samuel E Begg
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Korea
- Australian Research Council Centre of Excellence in Future Low-Energy Electronics Technologies, School of Mathematics and Physics, University of Queensland, St. Lucia, Queensland 4072, Australia
| | - Matthew J Davis
- Australian Research Council Centre of Excellence in Future Low-Energy Electronics Technologies, School of Mathematics and Physics, University of Queensland, St. Lucia, Queensland 4072, Australia
| | - Matthew T Reeves
- Australian Research Council Centre of Excellence in Future Low-Energy Electronics Technologies, School of Mathematics and Physics, University of Queensland, St. Lucia, Queensland 4072, Australia
| |
Collapse
|
3
|
Zhu Y, Semisalov B, Krstulovic G, Nazarenko S. Self-similar evolution of wave turbulence in Gross-Pitaevskii system. Phys Rev E 2023; 108:064207. [PMID: 38243462 DOI: 10.1103/physreve.108.064207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2023] [Accepted: 11/22/2023] [Indexed: 01/21/2024]
Abstract
We study the universal nonstationary evolution of wave turbulence (WT) in Bose-Einstein condensates (BECs). Their temporal evolution can exhibit different kinds of self-similar behavior corresponding to a large-time asymptotic of the system or to a finite-time blowup. We identify self-similar regimes in BECs by numerically simulating the forced and unforced Gross-Pitaevskii equation (GPE) and the associated wave kinetic equation (WKE) for the direct and inverse cascades, respectively. In both the GPE and the WKE simulations for the direct cascade, we observe the first-kind self-similarity that is fully determined by energy conservation. For the inverse cascade evolution, we verify the existence of a self-similar evolution of the second kind describing self-accelerating dynamics of the spectrum leading to blowup at the zero mode (condensate) at a finite time. We believe that the universal self-similar spectra found in the present paper are as important and relevant for understanding the BEC turbulence in past and future experiments as the commonly studied stationary Kolmogorov-Zakharov (KZ) spectra.
Collapse
Affiliation(s)
- Ying Zhu
- Université Côte d'Azur, CNRS, Institut de Physique de Nice (INPHYNI), 17 rue Julien Lauprêtre 06200 Nice, France
| | - Boris Semisalov
- Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Boulevard de l'Observatoire CS 34229-F 06304 Nice Cedex 4, France
- Sobolev Institute of Mathematics SB RAS, 4 Academician Koptyug Avenue, 630090 Novosibirsk, Russia
- Federal Research Center for Information and Computational Technologies, 6 Academician Lavrentyev Avenue, 630090 Novosibirsk, Russia
| | - Giorgio Krstulovic
- Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Boulevard de l'Observatoire CS 34229-F 06304 Nice Cedex 4, France
| | - Sergey Nazarenko
- Université Côte d'Azur, CNRS, Institut de Physique de Nice (INPHYNI), 17 rue Julien Lauprêtre 06200 Nice, France
| |
Collapse
|
4
|
Siovitz I, Lannig S, Deller Y, Strobel H, Oberthaler MK, Gasenzer T. Universal Dynamics of Rogue Waves in a Quenched Spinor Bose Condensate. PHYSICAL REVIEW LETTERS 2023; 131:183402. [PMID: 37977625 DOI: 10.1103/physrevlett.131.183402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 10/10/2023] [Indexed: 11/19/2023]
Abstract
Isolated many-body systems far from equilibrium may exhibit scaling dynamics with universal exponents indicating the proximity of the time evolution to a nonthermal fixed point. We find universal dynamics connected with the occurrence of extreme wave excitations in the mutually coupled magnetic components of a spinor gas which propagate in an effectively random potential. The frequency of these rogue waves is affected by the time-varying spatial correlation length of the potential, giving rise to an additional exponent δ_{c}≃1/3 for temporal scaling, which is different from the exponent β_{V}≃1/4 characterizing the scaling of the correlation length ℓ_{V}∼t^{β_{V}} in time. As a result of the caustics, i.e., focusing events, real-time instanton defects appear in the Larmor phase of the spin-1 system as vortices in space and time. The temporal correlations governing the instanton occurrence frequency scale as t^{δ_{I}}. This suggests that the universality class of a nonthermal fixed point could be characterized by different, mutually related exponents defining the evolution in time and space, respectively. Our results have a strong relevance for understanding pattern coarsening from first principles and potential implications for dynamics ranging from the early Universe to geophysical dynamics and microphysics.
Collapse
Affiliation(s)
- Ido Siovitz
- Kirchhoff-Institut für Physik, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Stefan Lannig
- Kirchhoff-Institut für Physik, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Yannick Deller
- Kirchhoff-Institut für Physik, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Helmut Strobel
- Kirchhoff-Institut für Physik, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Markus K Oberthaler
- Kirchhoff-Institut für Physik, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Thomas Gasenzer
- Kirchhoff-Institut für Physik, Ruprecht-Karls Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| |
Collapse
|
5
|
Dogra LH, Martirosyan G, Hilker TA, Glidden JAP, Etrych J, Cao A, Eigen C, Smith RP, Hadzibabic Z. Universal equation of state for wave turbulence in a quantum gas. Nature 2023; 620:521-524. [PMID: 37495696 DOI: 10.1038/s41586-023-06240-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2022] [Accepted: 05/19/2023] [Indexed: 07/28/2023]
Abstract
Boyle's 1662 observation that the volume of a gas is, at constant temperature, inversely proportional to pressure, offered a prototypical example of how an equation of state (EoS) can succinctly capture key properties of a many-particle system. Such relationships are now cornerstones of equilibrium thermodynamics1. Extending thermodynamic concepts to far-from-equilibrium systems is of great interest in various contexts, including glasses2,3, active matter4-7 and turbulence8-11, but is in general an open problem. Here, using a homogeneous ultracold atomic Bose gas12, we experimentally construct an EoS for a turbulent cascade of matter waves13,14. Under continuous forcing at a large length scale and dissipation at a small one, the gas exhibits a non-thermal, but stationary, state, which is characterized by a power-law momentum distribution15 sustained by a scale-invariant momentum-space energy flux16. We establish the amplitude of the momentum distribution and the underlying energy flux as equilibrium-like state variables, related by an EoS that does not depend on the details of the energy injection or dissipation, or on the history of the system. Moreover, we show that the equations of state for a wide range of interaction strengths and gas densities can be empirically scaled onto each other. This results in a universal dimensionless EoS that sets benchmarks for the theory and should also be relevant for other turbulent systems.
Collapse
Affiliation(s)
- Lena H Dogra
- Cavendish Laboratory, University of Cambridge, Cambridge, UK.
| | | | - Timon A Hilker
- Cavendish Laboratory, University of Cambridge, Cambridge, UK
- Max-Planck-Institut für Quantenoptik, Garching, Germany
| | | | - Jiří Etrych
- Cavendish Laboratory, University of Cambridge, Cambridge, UK
| | - Alec Cao
- Cavendish Laboratory, University of Cambridge, Cambridge, UK
| | - Christoph Eigen
- Cavendish Laboratory, University of Cambridge, Cambridge, UK.
| | | | | |
Collapse
|
6
|
Zhu Y, Semisalov B, Krstulovic G, Nazarenko S. Direct and Inverse Cascades in Turbulent Bose-Einstein Condensates. PHYSICAL REVIEW LETTERS 2023; 130:133001. [PMID: 37067330 DOI: 10.1103/physrevlett.130.133001] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2022] [Revised: 11/04/2022] [Accepted: 02/21/2023] [Indexed: 06/19/2023]
Abstract
When a Bose-Einstein condensate (BEC) is driven out of equilibrium, density waves interact nonlinearly and trigger turbulent cascades. In a turbulent BEC, energy is transferred toward small scales by a direct cascade, whereas the number of particles displays an inverse cascade toward large scales. In this work, we study analytically and numerically the direct and inverse cascades in wave-turbulent BECs. We analytically derive the Kolmogorov-Zakharov spectra, including the log correction to the direct cascade scaling and the universal prefactor constants for both cascades. We test and corroborate our predictions using high-resolution numerical simulations of the forced-dissipated Gross-Pitaevskii model in a periodic box and the corresponding wave-kinetic equation. Theoretical predictions and data are in excellent agreement, without adjustable parameters. Moreover, in order to connect with experiments, we test and validate our theoretical predictions using the Gross-Pitaevskii model with a confining cubic trap. Our results explain previous experimental observations and suggest new settings for future studies.
Collapse
Affiliation(s)
- Ying Zhu
- Université Côte d'Azur, CNRS, Institut de Physique de Nice (INPHYNI), Parc Valrose, 06108 Nice, France
| | - Boris Semisalov
- Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Boulevard de l'Observatoire CS 34229-F 06304 Nice Cedex 4, France
- Novosibirsk State University, 1 Pirogova street, 630090 Novosibirsk, Russia
- Sobolev Institute of Mathematics SB RAS, 4 Academician Koptyug Avenue, 630090 Novosibirsk, Russia
| | - Giorgio Krstulovic
- Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Boulevard de l'Observatoire CS 34229-F 06304 Nice Cedex 4, France
| | - Sergey Nazarenko
- Université Côte d'Azur, CNRS, Institut de Physique de Nice (INPHYNI), Parc Valrose, 06108 Nice, France
| |
Collapse
|
7
|
Gałka M, Christodoulou P, Gazo M, Karailiev A, Dogra N, Schmitt J, Hadzibabic Z. Emergence of Isotropy and Dynamic Scaling in 2D Wave Turbulence in a Homogeneous Bose Gas. PHYSICAL REVIEW LETTERS 2022; 129:190402. [PMID: 36399756 DOI: 10.1103/physrevlett.129.190402] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2022] [Revised: 08/24/2022] [Accepted: 09/14/2022] [Indexed: 06/16/2023]
Abstract
We realize a turbulent cascade of wave excitations in a homogeneous 2D Bose gas and probe on all relevant time and length scales how it builds up from small to large momenta, until the system reaches a steady state with matching energy injection and dissipation. This all-scales view directly reveals the two theoretically expected cornerstones of turbulence formation-the emergence of statistical momentum-space isotropy under anisotropic forcing and the spatiotemporal scaling of the momentum distribution at times before any energy is dissipated.
Collapse
Affiliation(s)
- Maciej Gałka
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Panagiotis Christodoulou
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Martin Gazo
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Andrey Karailiev
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Nishant Dogra
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Julian Schmitt
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
- Institut für Angewandte Physik, Universität Bonn, Wegelerstraße 8, 53115 Bonn, Germany
| | - Zoran Hadzibabic
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| |
Collapse
|
8
|
Zhu Y, Semisalov B, Krstulovic G, Nazarenko S. Testing wave turbulence theory for the Gross-Pitaevskii system. Phys Rev E 2022; 106:014205. [PMID: 35974496 DOI: 10.1103/physreve.106.014205] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2021] [Accepted: 05/04/2022] [Indexed: 06/15/2023]
Abstract
We test the predictions of the theory of weak wave turbulence by performing numerical simulations of the Gross-Pitaevskii equation (GPE) and the associated wave-kinetic equation (WKE). We consider an initial state localized in Fourier space, and we confront the solutions of the WKE obtained numerically with GPE data for both the wave-action spectrum and the probability density functions (PDFs) of the Fourier mode intensities. We find that the temporal evolution of the GPE data is accurately predicted by the WKE, with no adjustable parameters, for about two nonlinear kinetic times. Qualitative agreement between the GPE and the WKE persists also for longer times with some quantitative deviations that may be attributed to the combination of a breakdown of the theoretical assumptions underlying the WKE as well as numerical issues. Furthermore, we study how the wave statistics evolves toward Gaussianity in a timescale of the order of the kinetic time. The excellent agreement between direct numerical simulations of the GPE and the WKE provides a solid foundation to the theory of weak wave turbulence.
Collapse
Affiliation(s)
- Ying Zhu
- Université Côte d'Azur, CNRS, Institut de Physique de Nice (INPHYNI), Parc Valrose, 06108 Nice, France
| | - Boris Semisalov
- Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Boulevard de l'Observatoire CS 34229 - F 06304 Nice Cedex 4, France
- Novosibirsk State University, 1 Pirogova street, 630090 Novosibirsk, Russia
- Sobolev Institute of Mathematics SB RAS, 4 Academician Koptyug Avenue, 630090 Novosibirsk, Russia
| | - Giorgio Krstulovic
- Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Boulevard de l'Observatoire CS 34229 - F 06304 Nice Cedex 4, France
| | - Sergey Nazarenko
- Université Côte d'Azur, CNRS, Institut de Physique de Nice (INPHYNI), Parc Valrose, 06108 Nice, France
| |
Collapse
|
9
|
Hilker TA, Dogra LH, Eigen C, Glidden JAP, Smith RP, Hadzibabic Z. First and Second Sound in a Compressible 3D Bose Fluid. PHYSICAL REVIEW LETTERS 2022; 128:223601. [PMID: 35714252 DOI: 10.1103/physrevlett.128.223601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/31/2021] [Accepted: 04/12/2022] [Indexed: 06/15/2023]
Abstract
The two-fluid model is fundamental for the description of superfluidity. In the nearly incompressible liquid regime, it successfully describes first and second sound, corresponding, respectively, to density and entropy waves, in both liquid helium and unitary Fermi gases. Here, we study the two sounds in the opposite regime of a highly compressible fluid, using an ultracold ^{39}K Bose gas in a three-dimensional box trap. We excite the longest-wavelength mode of our homogeneous gas, and observe two distinct resonant oscillations below the critical temperature, of which only one persists above it. In a microscopic mode-structure analysis, we find agreement with the hydrodynamic theory, where first and second sound involve density oscillations dominated by, respectively, thermal and condensed atoms. Varying the interaction strength, we explore the crossover from hydrodynamic to collisionless behavior in a normal gas.
Collapse
Affiliation(s)
- Timon A Hilker
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Lena H Dogra
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Christoph Eigen
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Jake A P Glidden
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Robert P Smith
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Zoran Hadzibabic
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| |
Collapse
|
10
|
Griffin A, Krstulovic G, L'vov VS, Nazarenko S. Energy Spectrum of Two-Dimensional Acoustic Turbulence. PHYSICAL REVIEW LETTERS 2022; 128:224501. [PMID: 35714230 DOI: 10.1103/physrevlett.128.224501] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2021] [Revised: 02/23/2022] [Accepted: 04/20/2022] [Indexed: 06/15/2023]
Abstract
We report an exact unique constant-flux power-law analytical solution of the wave kinetic equation for the turbulent energy spectrum, E(k)=C_{1}sqrt[ϵac_{s}]/k, of acoustic waves in 2D with almost linear dispersion law, ω_{k}=c_{s}k[1+(ak)^{2}], ak≪1. Here, ϵ is the energy flux over scales, and C_{1} is the universal constant which was found analytically. Our theory describes, for example, acoustic turbulence in 2D Bose-Einstein condensates. The corresponding 3D counterpart of turbulent acoustic spectrum was found over half a century ago, however, due to the singularity in 2D, no solution has been obtained until now. We show the spectrum E(k) is realizable in direct numerical simulations of forced-dissipated Gross-Pitaevskii equation in the presence of strong condensate.
Collapse
Affiliation(s)
- Adam Griffin
- Université Côte d'Azur, Institut de Physique de Nice (INPHYNI), Parc Valrose, 06108 Nice, France
| | - Giorgio Krstulovic
- Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Boulevard de l'Observatoire CS 34229-F 06304 NICE Cedex 4, France
| | - Victor S L'vov
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Sergey Nazarenko
- Université Côte d'Azur, Institut de Physique de Nice (INPHYNI), Parc Valrose, 06108 Nice, France
| |
Collapse
|
11
|
Characteristic Length Scale during the Time Evolution of a Turbulent Bose-Einstein Condensate. Symmetry (Basel) 2021. [DOI: 10.3390/sym13101865] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Quantum turbulence is characterized by many degrees of freedom interacting non-linearly to produce disordered states, both in space and in time. In this work, we investigate the decaying regime of quantum turbulence in a trapped Bose-Einstein condensate. We present an alternative way of exploring this phenomenon by defining and computing a characteristic length scale, which possesses relevant characteristics to study the establishment of the quantum turbulent regime. We reconstruct the three-dimensional momentum distributions with the inverse Abel transform, as we have done successfully in other works. We present our analysis with both the two- and three-dimensional momentum distributions, discussing their similarities and differences. We argue that the characteristic length allows us to intuitively visualize the time evolution of the turbulent state.
Collapse
|
12
|
Zhang J, Eigen C, Zheng W, Glidden JAP, Hilker TA, Garratt SJ, Lopes R, Cooper NR, Hadzibabic Z, Navon N. Many-Body Decay of the Gapped Lowest Excitation of a Bose-Einstein Condensate. PHYSICAL REVIEW LETTERS 2021; 126:060402. [PMID: 33635703 DOI: 10.1103/physrevlett.126.060402] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2020] [Revised: 12/09/2020] [Accepted: 01/11/2021] [Indexed: 06/12/2023]
Abstract
We study the decay mechanism of the gapped lowest-lying axial excitation of a quasipure atomic Bose-Einstein condensate confined in a cylindrical box trap. Owing to the absence of accessible lower-energy modes, or direct coupling to an external bath, this excitation is protected against one-body (linear) decay, and the damping mechanism is exclusively nonlinear. We develop a universal theoretical model that explains this fundamentally nonlinear damping as a process whereby two quanta of the gapped lowest excitation mode couple to a higher-energy mode, which subsequently decays into a continuum. We find quantitative agreement between our experiments and the predictions of this model. Finally, by strongly driving the system below its (lowest) resonant frequency, we observe third-harmonic generation, a hallmark of nonlinear behavior.
Collapse
Affiliation(s)
- Jinyi Zhang
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Christoph Eigen
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Wei Zheng
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Jake A P Glidden
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Timon A Hilker
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Samuel J Garratt
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
- Theoretical Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Raphael Lopes
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Nigel R Cooper
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Zoran Hadzibabic
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Nir Navon
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| |
Collapse
|
13
|
Madeira L, García-Orozco AD, dos Santos FEA, Bagnato VS. Entropy of a Turbulent Bose-Einstein Condensate. ENTROPY 2020; 22:e22090956. [PMID: 33286725 PMCID: PMC7597245 DOI: 10.3390/e22090956] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/30/2020] [Revised: 08/20/2020] [Accepted: 08/26/2020] [Indexed: 11/16/2022]
Abstract
Quantum turbulence deals with the phenomenon of turbulence in quantum fluids, such as superfluid helium and trapped Bose-Einstein condensates (BECs). Although much progress has been made in understanding quantum turbulence, several fundamental questions remain to be answered. In this work, we investigated the entropy of a trapped BEC in several regimes, including equilibrium, small excitations, the onset of turbulence, and a turbulent state. We considered the time evolution when the system is perturbed and let to evolve after the external excitation is turned off. We derived an expression for the entropy consistent with the accessible experimental data, which is, using the assumption that the momentum distribution is well-known. We related the excitation amplitude to different stages of the perturbed system, and we found distinct features of the entropy in each of them. In particular, we observed a sudden increase in the entropy following the establishment of a particle cascade. We argue that entropy and related quantities can be used to investigate and characterize quantum turbulence.
Collapse
Affiliation(s)
- Lucas Madeira
- Instituto de Física de São Carlos, Universidade de São Paulo, CP 369, São Carlos, São Paulo 13560-970, Brazil; (A.D.G.-O.); (V.S.B.)
- Correspondence:
| | - Arnol Daniel García-Orozco
- Instituto de Física de São Carlos, Universidade de São Paulo, CP 369, São Carlos, São Paulo 13560-970, Brazil; (A.D.G.-O.); (V.S.B.)
| | | | - Vanderlei Salvador Bagnato
- Instituto de Física de São Carlos, Universidade de São Paulo, CP 369, São Carlos, São Paulo 13560-970, Brazil; (A.D.G.-O.); (V.S.B.)
- Hagler Fellow, Department of Biomedical Engineering, Texas A&M University, College Station, TX 77843, USA
| |
Collapse
|
14
|
Varga E, Vadakkumbatt V, Shook AJ, Kim PH, Davis JP. Observation of Bistable Turbulence in Quasi-Two-Dimensional Superflow. PHYSICAL REVIEW LETTERS 2020; 125:025301. [PMID: 32701340 DOI: 10.1103/physrevlett.125.025301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2020] [Revised: 04/15/2020] [Accepted: 06/02/2020] [Indexed: 06/11/2023]
Abstract
Turbulent flow restricted to two dimensions can spontaneously develop order on large scales, defying entropy expectations and in sharp contrast with turbulence in three dimensions where nonlinear turbulent processes act to destroy large-scale order. In this work we report the observation of unusual turbulent behavior in steady-state flow of superfluid ^{4}He-a liquid with vanishing viscosity and discrete vorticity-in a nearly two-dimensional channel. Surprisingly, for a range of experimental parameters, turbulence is observed to exist in two bistable states. This bistability can be well explained by the appearance of large-scale regions of flow of opposite vorticity.
Collapse
Affiliation(s)
- E Varga
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - V Vadakkumbatt
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - A J Shook
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - P H Kim
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - J P Davis
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| |
Collapse
|
15
|
Navon N, Eigen C, Zhang J, Lopes R, Gaunt AL, Fujimoto K, Tsubota M, Smith RP, Hadzibabic Z. Synthetic dissipation and cascade fluxes in a turbulent quantum gas. Science 2019; 366:382-385. [DOI: 10.1126/science.aau6103] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2018] [Accepted: 09/24/2019] [Indexed: 11/02/2022]
Abstract
Scale-invariant fluxes are the defining property of turbulent cascades, but their direct measurement is a challenging experimental problem. Here we perform such a measurement for a direct energy cascade in a turbulent quantum gas. Using a time-periodic force, we inject energy at a large length scale and generate a cascade in a uniformly trapped three-dimensional Bose gas. The adjustable trap depth provides a high-momentum cutoff kD, which realizes a synthetic dissipation scale. This gives us direct access to the particle flux across a momentum shell of radius kD, and the tunability of kD allows for a clear demonstration of the zeroth law of turbulence. Moreover, our time-resolved measurements give unique access to the pre–steady-state dynamics, when the cascade front propagates in momentum space.
Collapse
Affiliation(s)
- Nir Navon
- Department of Physics, Yale University, New Haven, CT 06520, USA
| | - Christoph Eigen
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK
| | - Jinyi Zhang
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK
| | - Raphael Lopes
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK
| | - Alexander L. Gaunt
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK
- Microsoft Research, Cambridge CB1 2FB, UK
| | - Kazuya Fujimoto
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Makoto Tsubota
- Department of Physics and Nambu Yoichiro Institute of Theoretical and Experimental Physics, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-Ku, Osaka 558-8585, Japan
| | - Robert P. Smith
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK
- Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK
| | - Zoran Hadzibabic
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK
| |
Collapse
|
16
|
Johnstone SP, Groszek AJ, Starkey PT, Billington CJ, Simula TP, Helmerson K. Evolution of large-scale flow from turbulence in a two-dimensional superfluid. Science 2019; 364:1267-1271. [DOI: 10.1126/science.aat5793] [Citation(s) in RCA: 77] [Impact Index Per Article: 15.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2018] [Accepted: 06/06/2019] [Indexed: 11/02/2022]
Abstract
Nonequilibrium interacting systems can evolve to exhibit large-scale structure and order. In two-dimensional turbulent flow, the seemingly random swirling motion of a fluid can evolve toward persistent large-scale vortices. To explain such behavior, Lars Onsager proposed a statistical hydrodynamic model based on quantized vortices. Here, we report on the experimental confirmation of Onsager’s model. We dragged a grid barrier through an oblate superfluid Bose–Einstein condensate to generate nonequilibrium distributions of vortices. We observed signatures of an inverse energy cascade driven by the evaporative heating of vortices, leading to steady-state configurations characterized by negative absolute temperatures. Our results open a pathway for quantitative studies of emergent structures in interacting quantum systems driven far from equilibrium.
Collapse
Affiliation(s)
- Shaun P. Johnstone
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
| | - Andrew J. Groszek
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
| | - Philip T. Starkey
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
| | - Christopher J. Billington
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
- Joint Quantum Institute, National Institute of Standards and Technology, and University of Maryland, Gaithersburg, MD 20899, USA
| | - Tapio P. Simula
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
| | - Kristian Helmerson
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Monash University, Victoria 3800, Australia
| |
Collapse
|