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Bhowmik A, Alon OE. Coupled-cluster theory for trapped bosonic mixtures. J Chem Phys 2024; 160:044105. [PMID: 38258928 DOI: 10.1063/5.0176145] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2023] [Accepted: 12/26/2023] [Indexed: 01/24/2024] Open
Abstract
We develop a coupled-cluster theory for bosonic mixtures of binary species in external traps, providing a promising theoretical approach to demonstrate highly accurately the many-body physics of mixtures of Bose-Einstein condensates. The coupled-cluster wavefunction for the binary species is obtained when an exponential cluster operator eT, where T = T(1) + T(2) + T(12) and T(1) accounts for excitations in species-1, T(2) for excitations in species-2, and T(12) for combined excitations in both species, acts on the ground state configuration prepared by accumulating all bosons in a single orbital for each species. We have explicitly derived the working equations for bosonic mixtures by truncating the cluster operator up to the single and double excitations and using arbitrary sets of orthonormal orbitals for each of the species. Furthermore, the comparatively simplified version of the working equations are formulated using the Fock-like operators. Finally, using an exactly solvable many-body model for bosonic mixtures that exists in the literature allows us to implement and test the performance and accuracy of the coupled-cluster theory for situations with balanced as well as imbalanced boson numbers and for weak to moderately strong intra- and interspecies interaction strengths. The comparison between our computed results using coupled-cluster theory with the respective analytical exact results displays remarkable agreement exhibiting excellent success of the coupled-cluster theory for bosonic mixtures. All in all, the correlation exhaustive coupled-cluster theory shows encouraging results and could be a promising approach in paving the way for high-accuracy modeling of various bosonic mixture systems.
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Affiliation(s)
- Anal Bhowmik
- Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, Norman, Oklahoma 73019, USA
- Center for Quantum Research and Technology, The University of Oklahoma, Norman, Oklahoma 73019, USA
- Department of Physics, University of Haifa, Haifa 3498838, Israel
- Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Haifa 3498838, Israel
| | - Ofir E Alon
- Department of Physics, University of Haifa, Haifa 3498838, Israel
- Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Haifa 3498838, Israel
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2
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Dutta S, Lode AUJ, Alon OE. Fragmentation and correlations in a rotating Bose-Einstein condensate undergoing breakup. Sci Rep 2023; 13:3343. [PMID: 36849498 PMCID: PMC9971194 DOI: 10.1038/s41598-023-29516-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2022] [Accepted: 02/06/2023] [Indexed: 03/01/2023] Open
Abstract
The theoretical investigation of rotating Bose-Einstein condensates has mainly focused on the emergence of quantum vortex states and the condensed properties of such systems. In the present work, we concentrate on other facets by examining the impact of rotation on the ground state of weakly interacting bosons confined in anharmonic potentials computed both at the mean-field level and particularly at the many-body level of theory. For the many-body computations, we employ the well-established many-body method known as the multiconfigurational time-dependent Hartree method for bosons. We present how various degrees of fragmentation can be generated following the breakup of the ground state densities in anharmonic traps without ramping up a potential barrier for strong rotations. The breakup of the densities is found to be associated with the acquisition of angular momentum in the condensate due to the rotation. In addition to fragmentation, the presence of many-body correlations is examined by computing the variances of the many-particle position and momentum operators. For strong rotations, the many-body variances become smaller than their mean-field counterparts, and one even finds a scenario with opposite anisotropies of the mean-field and many-body variances. Further, it is observed that for higher discrete symmetric systems of order k, namely three-fold and four-fold symmetry, breakup to k sub-clouds and emergence of k-fold fragmentation take place. All in all, we provide a thorough many-body investigation of how and which correlations build up when a trapped Bose-Einstein condensate breaks up under rotation.
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Affiliation(s)
- Sunayana Dutta
- Department of Physics, University of Haifa, 3498838, Haifa, Israel.
- Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, 3498838, Haifa, Israel.
| | - Axel U J Lode
- Institute of Physics, Albert-Ludwig University of Freiburg, Hermann-Herder-Strasse 3, 79104, Freiburg, Germany
| | - Ofir E Alon
- Department of Physics, University of Haifa, 3498838, Haifa, Israel
- Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, 3498838, Haifa, Israel
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Roy R, Chakrabarti B, Chavda ND, Lekala ML. Information theoretic measures for interacting bosons in optical lattice. Phys Rev E 2023; 107:024119. [PMID: 36932481 DOI: 10.1103/physreve.107.024119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2022] [Accepted: 01/19/2023] [Indexed: 06/18/2023]
Abstract
This work reports the different information theoretic measures, i.e., Shannon information entropy, order, disorder, complexity, and their dynamical measure for the interacting bosons in an optical lattice with both commensurate and incommensurate filling factor. We solve the many-body Schrödinger equation from first principles by multiconfigurational time-dependent Hartree method which calculates all the measures with high level of accuracy. We find for both relaxed state as well as quenched state the López-Ruiz-Mancini-Calbet (LMC) measure of complexity is the most efficient depictor of superfluid (SF) to Mott-insulator transition. In the quench dynamics, the distinct structure of LMC complexity can be used as a "figure of merit" to obtain the timescale of SF to Mott state entry, Mott holding time, and the Mott state to SF state entry in the successive cycles. We also find that fluctuations in the dynamics of LMC complexity measure for incommensurate filling clearly establish that superfluid to Mott-insulator transition is incomplete. We overall conclude that distinct structure in the complexity makes it more sensitive than the standard use of Shannon information entropy.
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Affiliation(s)
- Rhombik Roy
- Department of Physics, Presidency University, 86/1 College Street, Kolkata 700073, India
| | - Barnali Chakrabarti
- Department of Physics, Presidency University, 86/1 College Street, Kolkata 700073, India
| | - N D Chavda
- Department of Applied Physics, Faculty of Technology and Engineering, The Maharaja Sayajirao University of Baroda, Vadodara-390001, India
| | - M L Lekala
- Department of Physics, University of South Africa, P.O. Box 392, Pretoria 0003, South Africa
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Abstract
Recent studies have demonstrated that higher than two-body bath-impurity correlations are not important for quantitatively describing the ground state of the Bose polaron. Motivated by the above, we employ the so-called Gross Ansatz (GA) approach to unravel the stationary and dynamical properties of the homogeneous one-dimensional Bose-polaron for different impurity momenta and bath-impurity couplings. We explicate that the character of the equilibrium state crossovers from the quasi-particle Bose polaron regime to the collective-excitation stationary dark-bright soliton for varying impurity momentum and interactions. Following an interspecies interaction quench the temporal orthogonality catastrophe is identified, provided that bath-impurity interactions are sufficiently stronger than the intraspecies bath ones, thus generalizing the results of the confined case. This catastrophe originates from the formation of dispersive shock wave structures associated with the zero-range character of the bath-impurity potential. For initially moving impurities, a momentum transfer process from the impurity to the dispersive shock waves via the exerted drag force is demonstrated, resulting in a final polaronic state with reduced velocity. Our results clearly demonstrate the crucial role of non-linear excitations for determining the behavior of the one-dimensional Bose polaron.
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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]
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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.
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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
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Pyzh M, Keiler K, Mistakidis SI, Schmelcher P. Entangling Lattice-Trapped Bosons with a Free Impurity: Impact on Stationary and Dynamical Properties. ENTROPY (BASEL, SWITZERLAND) 2021; 23:290. [PMID: 33652970 PMCID: PMC7996946 DOI: 10.3390/e23030290] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/05/2021] [Revised: 02/22/2021] [Accepted: 02/23/2021] [Indexed: 01/07/2023]
Abstract
We address the interplay of few lattice trapped bosons interacting with an impurity atom in a box potential. For the ground state, a classification is performed based on the fidelity allowing to quantify the susceptibility of the composite system to structural changes due to the intercomponent coupling. We analyze the overall response at the many-body level and contrast it to the single-particle level. By inspecting different entropy measures we capture the degree of entanglement and intraspecies correlations for a wide range of intra- and intercomponent interactions and lattice depths. We also spatially resolve the imprint of the entanglement on the one- and two-body density distributions showcasing that it accelerates the phase separation process or acts against spatial localization for repulsive and attractive intercomponent interactions, respectively. The many-body effects on the tunneling dynamics of the individual components, resulting from their counterflow, are also discussed. The tunneling period of the impurity is very sensitive to the value of the impurity-medium coupling due to its effective dressing by the few-body medium. Our work provides implications for engineering localized structures in correlated impurity settings using species selective optical potentials.
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Affiliation(s)
- Maxim Pyzh
- Center for Optical Quantum Technologies, Department of Physics, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany; (M.P.); (K.K.); (S.I.M.)
| | - Kevin Keiler
- Center for Optical Quantum Technologies, Department of Physics, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany; (M.P.); (K.K.); (S.I.M.)
| | - Simeon I. Mistakidis
- Center for Optical Quantum Technologies, Department of Physics, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany; (M.P.); (K.K.); (S.I.M.)
| | - Peter Schmelcher
- Center for Optical Quantum Technologies, Department of Physics, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany; (M.P.); (K.K.); (S.I.M.)
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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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
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Analysis of a Trapped Bose–Einstein Condensate in Terms of Position, Momentum, and Angular-Momentum Variance. Symmetry (Basel) 2019. [DOI: 10.3390/sym11111344] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Abstract
We analyze, analytically and numerically, the position, momentum, and in particular the angular-momentum variance of a Bose–Einstein condensate (BEC) trapped in a two-dimensional anisotropic trap for static and dynamic scenarios. Explicitly, we study the ground state of the anisotropic harmonic-interaction model in two spatial dimensions analytically and the out-of-equilibrium dynamics of repulsive bosons in tilted two-dimensional annuli numerically accurately by using the multiconfigurational time-dependent Hartree for bosons method. The differences between the variances at the mean-field level, which are attributed to the shape of the BEC, and the variances at the many-body level, which incorporate depletion, are used to characterize position, momentum, and angular-momentum correlations in the BEC for finite systems and at the limit of an infinite number of particles where the bosons are 100 % condensed. Finally, we also explore inter-connections between the variances.
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Köhler F, Keiler K, Mistakidis SI, Meyer HD, Schmelcher P. Dynamical pruning of the non-equilibrium quantum dynamics of trapped ultracold bosons. J Chem Phys 2019. [DOI: 10.1063/1.5104344] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- F. Köhler
- Center for Optical Quantum Technologies, Department of Physics, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- Hamburg Center for Ultrafast Imaging, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - K. Keiler
- Center for Optical Quantum Technologies, Department of Physics, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - S. I. Mistakidis
- Center for Optical Quantum Technologies, Department of Physics, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - H.-D. Meyer
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany
| | - P. Schmelcher
- Center for Optical Quantum Technologies, Department of Physics, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- Hamburg Center for Ultrafast Imaging, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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11
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Levy A, Dou W, Rabani E, Limmer DT. A complete quasiclassical map for the dynamics of interacting fermions. J Chem Phys 2019; 150:234112. [DOI: 10.1063/1.5099987] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Amikam Levy
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
- The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Wenjie Dou
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
| | - Eran Rabani
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
- The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - David T. Limmer
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Kavli Energy NanoScience Institute, Berkeley, California 94720, USA
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12
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Mistakidis SI, Katsimiga GC, Koutentakis GM, Busch T, Schmelcher P. Quench Dynamics and Orthogonality Catastrophe of Bose Polarons. PHYSICAL REVIEW LETTERS 2019; 122:183001. [PMID: 31144905 DOI: 10.1103/physrevlett.122.183001] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2018] [Indexed: 06/09/2023]
Abstract
We monitor the correlated quench induced dynamical dressing of a spinor impurity repulsively interacting with a Bose-Einstein condensate. Inspecting the temporal evolution of the structure factor, three distinct dynamical regions arise upon increasing the interspecies interaction. These regions are found to be related to the segregated nature of the impurity and to the Ohmic character of the bath. It is shown that the impurity dynamics can be described by an effective potential that deforms from a harmonic to a double-well one when crossing the miscibility-immiscibility threshold. In particular, for miscible components the polaron formation is imprinted on the spectral response of the system. We further illustrate that for increasing interaction an orthogonality catastrophe occurs and the polaron picture breaks down. Then a dissipative motion of the impurity takes place leading to a transfer of energy to its environment. This process signals the presence of entanglement in the many-body system.
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Affiliation(s)
- S I Mistakidis
- Center for Optical Quantum Technologies, Department of Physics, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - G C Katsimiga
- Center for Optical Quantum Technologies, Department of Physics, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - G M Koutentakis
- Center for Optical Quantum Technologies, Department of Physics, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Th Busch
- Quantum Systems Unit, OIST Graduate University, Onna, Okinawa 904-0495, Japan
| | - P Schmelcher
- Center for Optical Quantum Technologies, Department of Physics, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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13
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Affiliation(s)
- Ofir E. Alon
- Department of Mathematics, University of Haifa, Haifa, Israel
- Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Haifa, Israel
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14
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Attractive Bose-Einstein condensates in anharmonic traps: Accurate numerical treatment and the intriguing physics of the variance. Chem Phys 2018. [DOI: 10.1016/j.chemphys.2018.09.029] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Chen J, Schurer JM, Schmelcher P. Entanglement Induced Interactions in Binary Mixtures. PHYSICAL REVIEW LETTERS 2018; 121:043401. [PMID: 30095960 DOI: 10.1103/physrevlett.121.043401] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2017] [Indexed: 06/08/2023]
Abstract
We establish a conceptual framework for the identification and the characterization of induced interactions in binary mixtures and reveal their intricate relation to entanglement between the components or species of the mixture. Exploiting an expansion in terms of the strength of the entanglement among the two species enables us to deduce an effective single-species description. In this way, we naturally incorporate the mutual feedback of the species and obtain induced interactions for both species which are effectively present among the particles of same type. Importantly, our approach incorporates few-body and inhomogeneous systems extending the scope of induced interactions where two particles interact via a bosonic bath-type environment. Employing the example of a one-dimensional ultracold Bose-Fermi mixture, we obtain induced Bose-Bose and Fermi-Fermi interactions with short-range attraction and long-range repulsion. With this, we show how beyond species mean-field physics visible in the two-body correlation functions can be understood via the induced interactions.
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Affiliation(s)
- J Chen
- 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
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - P Schmelcher
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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Mistakidis S, Koutentakis G, Schmelcher P. Bosonic quantum dynamics following a linear interaction quench in finite optical lattices of unit filling. Chem Phys 2018. [DOI: 10.1016/j.chemphys.2017.11.022] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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