1
|
Weike T, Manthe U. The multi-configurational time-dependent Hartree approach in optimized second quantization: thermal ensembles and statistical sampling. Chem Phys 2021. [DOI: 10.1016/j.chemphys.2021.111413] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
|
2
|
Lode AUJ, Dutta S, Lévêque C. Dynamics of Ultracold Bosons in Artificial Gauge Fields-Angular Momentum, Fragmentation, and the Variance of Entropy. ENTROPY (BASEL, SWITZERLAND) 2021; 23:392. [PMID: 33806185 PMCID: PMC8067171 DOI: 10.3390/e23040392] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/15/2020] [Revised: 02/26/2021] [Accepted: 03/11/2021] [Indexed: 11/16/2022]
Abstract
We consider the dynamics of two-dimensional interacting ultracold bosons triggered by suddenly switching on an artificial gauge field. The system is initialized in the ground state of a harmonic trapping potential. As a function of the strength of the applied artificial gauge field, we analyze the emergent dynamics by monitoring the angular momentum, the fragmentation as well as the entropy and variance of the entropy of absorption or single-shot images. We solve the underlying time-dependent many-boson Schrödinger equation using the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X). We find that the artificial gauge field implants angular momentum in the system. Fragmentation-multiple macroscopic eigenvalues of the reduced one-body density matrix-emerges in sync with the dynamics of angular momentum: the bosons in the many-body state develop non-trivial correlations. Fragmentation and angular momentum are experimentally difficult to assess; here, we demonstrate that they can be probed by statistically analyzing the variance of the image entropy of single-shot images that are the standard projective measurement of the state of ultracold atomic systems.
Collapse
Affiliation(s)
- Axel U. J. Lode
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany
| | - Sunayana Dutta
- Department of Mathematics, University of Haifa, Haifa 3498838, Israel;
- Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Haifa 3498838, Israel
| | - Camille Lévêque
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Stadionallee 2, 1020 Vienna, Austria;
- Wolfgang Pauli Institute c/o Faculty of Mathematics, University of Vienna, Oskar-Morgenstern Platz 1, 1090 Vienna, Austria
| |
Collapse
|
3
|
Weike T, Manthe U. The multi-configurational time-dependent Hartree approach in optimized second quantization: Imaginary time propagation and particle number conservation. J Chem Phys 2020; 152:034101. [DOI: 10.1063/1.5140984] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Thomas Weike
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
| | - Uwe Manthe
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
| |
Collapse
|
4
|
Sowiński T, Ángel García-March M. One-dimensional mixtures of several ultracold atoms: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:104401. [PMID: 31404916 DOI: 10.1088/1361-6633/ab3a80] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Recent theoretical and experimental progress on studying one-dimensional systems of bosonic, fermionic, and Bose-Fermi mixtures of a few ultracold atoms confined in traps is reviewed in the broad context of mesoscopic quantum physics. We pay special attention to limiting cases of very strong or very weak interactions and transitions between them. For bosonic mixtures, we describe the developments in systems of three and four atoms as well as different extensions to larger numbers of particles. We also briefly review progress in the case of spinor Bose gases of a few atoms. For fermionic mixtures, we discuss a special role of spin and present a detailed discussion of the two- and three-atom cases. We discuss the advantages and disadvantages of different computation methods applied to systems with intermediate interactions. In the case of very strong repulsion, close to the infinite limit, we discuss approaches based on effective spin chain descriptions. We also report on recent studies on higher-spin mixtures and inter-component attractive forces. For both statistics, we pay particular attention to impurity problems and mass imbalance cases. Finally, we describe the recent advances on trapped Bose-Fermi mixtures, which allow for a theoretical combination of previous concepts, well illustrating the importance of quantum statistics and inter-particle interactions. Lastly, we report on fundamental questions related to the subject which we believe will inspire further theoretical developments and experimental verification.
Collapse
Affiliation(s)
- Tomasz Sowiński
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, PL-02668 Warsaw, Poland
| | | |
Collapse
|
5
|
Cao L, Bolsinger V, Mistakidis SI, Koutentakis GM, Krönke S, Schurer JM, Schmelcher P. A unified ab initio approach to the correlated quantum dynamics of ultracold fermionic and bosonic mixtures. J Chem Phys 2018; 147:044106. [PMID: 28764383 DOI: 10.1063/1.4993512] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
We extent the recently developed Multi-Layer Multi-Configuration Time-Dependent Hartree method for Bosons for simulating the correlated quantum dynamics of bosonic mixtures to the fermionic sector and establish a unifying approach for the investigation of the correlated quantum dynamics of a mixture of indistinguishable particles, be it fermions or bosons. Relying on a multi-layer wave-function expansion, the resulting Multi-Layer Multi-Configuration Time-Dependent Hartree method for Mixtures (ML-MCTDHX) can be adapted to efficiently resolve system-specific intra- and inter-species correlations. The versatility and efficiency of ML-MCTDHX are demonstrated by applying it to the problem of colliding few-atom mixtures of both Bose-Fermi and Fermi-Fermi types. Thereby, we elucidate the role of correlations in the transmission and reflection properties of the collisional events. In particular, we present examples where the reflection (transmission) at the other atomic species is a correlation-dominated effect, i.e., it is suppressed in the mean-field approximation.
Collapse
Affiliation(s)
- L Cao
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - V Bolsinger
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - S I Mistakidis
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - G M Koutentakis
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - S Krönke
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - J M Schurer
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - P Schmelcher
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| |
Collapse
|
6
|
Manthe U. Wavepacket dynamics and the multi-configurational time-dependent Hartree approach. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:253001. [PMID: 28430111 DOI: 10.1088/1361-648x/aa6e96] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Multi-configurational time-dependent Hartree (MCTDH) based approaches are efficient, accurate, and versatile methods for high-dimensional quantum dynamics simulations. Applications range from detailed investigations of polyatomic reaction processes in the gas phase to high-dimensional simulations studying the dynamics of condensed phase systems described by typical solid state physics model Hamiltonians. The present article presents an overview of the different areas of application and provides a comprehensive review of the underlying theory. The concepts and guiding ideas underlying the MCTDH approach and its multi-mode and multi-layer extensions are discussed in detail. The general structure of the equations of motion is highlighted. The representation of the Hamiltonian and the correlated discrete variable representation (CDVR), which provides an efficient multi-dimensional quadrature in MCTDH calculations, are discussed. Methods which facilitate the calculation of eigenstates, the evaluation of correlation functions, and the efficient representation of thermal ensembles in MCTDH calculations are described. Different schemes for the treatment of indistinguishable particles in MCTDH calculations and recent developments towards a unified multi-layer MCTDH theory for systems including bosons and fermions are discussed.
Collapse
Affiliation(s)
- Uwe Manthe
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
| |
Collapse
|
7
|
Alcala DA, Glick JA, Carr LD. Entangled Dynamics in Macroscopic Quantum Tunneling of Bose-Einstein Condensates. PHYSICAL REVIEW LETTERS 2017; 118:210403. [PMID: 28598673 DOI: 10.1103/physrevlett.118.210403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2016] [Indexed: 06/07/2023]
Abstract
Tunneling of a quasibound state is a nonsmooth process in the entangled many-body case. Using time-evolving block decimation, we show that repulsive (attractive) interactions speed up (slow down) tunneling. While the escape time scales exponentially with small interactions, the maximization time of the von Neumann entanglement entropy between the remaining quasibound and escaped atoms scales quadratically. Stronger interactions require higher-order corrections. Entanglement entropy is maximized when about half the atoms have escaped.
Collapse
Affiliation(s)
- Diego A Alcala
- Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
| | - Joseph A Glick
- Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
| | - Lincoln D Carr
- Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
| |
Collapse
|
8
|
Manthe U, Weike T. On the multi-layer multi-configurational time-dependent Hartree approach for bosons and fermions. J Chem Phys 2017; 146:064117. [DOI: 10.1063/1.4975662] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
9
|
Potnis S, Ramos R, Maeda K, Carr LD, Steinberg AM. Interaction-Assisted Quantum Tunneling of a Bose-Einstein Condensate Out of a Single Trapping Well. PHYSICAL REVIEW LETTERS 2017; 118:060402. [PMID: 28234507 DOI: 10.1103/physrevlett.118.060402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2016] [Indexed: 06/06/2023]
Abstract
We experimentally study tunneling of Bose-condensed ^{87}Rb atoms prepared in a quasibound state and observe a nonexponential decay caused by interatomic interactions. A combination of a magnetic quadrupole trap and a thin 1.3 μm barrier created using a blue-detuned sheet of light is used to tailor traps with controllable depth and tunneling rate. The escape dynamics strongly depend on the mean-field energy, which gives rise to three distinct regimes-classical spilling over the barrier, quantum tunneling, and decay dominated by background losses. We show that the tunneling rate depends exponentially on the chemical potential. Our results show good agreement with numerical solutions of the 3D Gross-Pitaevskii equation.
Collapse
Affiliation(s)
- Shreyas Potnis
- Centre for Quantum Information and Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 1A7, Canada
| | - Ramon Ramos
- Centre for Quantum Information and Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 1A7, Canada
| | - Kenji Maeda
- Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
| | - Lincoln D Carr
- Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
| | - Aephraim M Steinberg
- Centre for Quantum Information and Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 1A7, Canada
- Canadian Institute For Advanced Research, 180 Dundas Street West, Toronto, Ontario M5G 1Z8, Canada
| |
Collapse
|
10
|
Weiner SE, Tsatsos MC, Cederbaum LS, Lode AUJ. Phantom vortices: hidden angular momentum in ultracold dilute Bose-Einstein condensates. Sci Rep 2017; 7:40122. [PMID: 28091520 PMCID: PMC5238373 DOI: 10.1038/srep40122] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2016] [Accepted: 12/02/2016] [Indexed: 11/24/2022] Open
Abstract
Vortices are essential to angular momentum in quantum systems such as ultracold atomic gases. The existence of quantized vorticity in bosonic systems stimulated the development of the Gross-Pitaevskii mean-field approximation. However, the true dynamics of angular momentum in finite, interacting many-body systems like trapped Bose-Einstein condensates is enriched by the emergence of quantum correlations whose description demands more elaborate methods. Herein we theoretically investigate the full many-body dynamics of the acquisition of angular momentum by a gas of ultracold bosons in two dimensions using a standard rotation procedure. We demonstrate the existence of a novel mode of quantized vorticity, which we term the phantom vortex. Contrary to the conventional mean-field vortex, can be detected as a topological defect of spatial coherence, but not of the density. We describe previously unknown many-body mechanisms of vortex nucleation and show that angular momentum is hidden in phantom vortices modes which so far seem to have evaded experimental detection. This phenomenon is likely important in the formation of the Abrikosov lattice and the onset of turbulence in superfluids.
Collapse
Affiliation(s)
- Storm E Weiner
- Department of Physics, University of California at Berkeley, CA, USA
| | - Marios C Tsatsos
- Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, São Paulo, Brazil
| | - Lorenz S Cederbaum
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Germany
| | - Axel U J Lode
- Department of Physics, University of Basel, Switzerland
| |
Collapse
|
11
|
Alon OE, Streltsov AI, Cederbaum LS. Unified view on linear response of interacting identical and distinguishable particles from multiconfigurational time-dependent Hartree methods. J Chem Phys 2014; 140:034108. [DOI: 10.1063/1.4860970] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
|