Longitudinal and transversal resonant tunneling of interacting bosons in a two-dimensional Josephson junction

AbstractWe unravel the out-of-equilibrium quantum dynamics of a few interacting bosonic clouds in a two-dimensional asymmetric double-well potential at the resonant tunneling scenario. At the single-particle level of resonant tunneling, particles tunnel under the barrier from, typically, the ground-state in the left well to an excited state in the right well, i.e., states of different shapes and properties are coupled when their one-particle energies coincide. In two spatial dimensions, two types of resonant tunneling processes are possible, to which we refer to as longitudinal and transversal resonant tunneling. Longitudinal resonant tunneling implies that the state in the right well is longitudinally-excited with respect to the state in the left well, whereas transversal resonant tunneling implies that the former is transversely-excited with respect to the latter. We show that interaction between bosons makes resonant tunneling phenomena in two spatial dimensions profoundly rich, and analyze these phenomena in terms of the loss of coherence of the junction and development of fragmentation, and coupling between transverse and longitudinal degrees-of-freedom and excitations. To this end, a detailed analysis of the tunneling dynamics is performed by exploring the time evolution of a few physical quantities, namely, the survival probability, occupation numbers of the reduced one-particle density matrix, and the many-particle position, momentum, and angular-momentum variances. To accurately calculate these physical quantities from the time-dependent many-boson wavefunction, we apply a well-established many-body method, the multiconfigurational time-dependent Hartree for bosons (MCTDHB), which incorporates quantum correlations exhaustively. By comparing the survival probabilities and variances at the mean-field and many-body levels of theory and investigating the development of fragmentation, we identify the detailed mechanisms of many-body longitudinal and transversal resonant tunneling in two dimensional asymmetric double-wells. In particular, we find that the position and momentum variances along the transversal direction are almost negligible at the longitudinal resonant tunneling, whereas they are substantial at the transversal resonant tunneling which is caused by the combination of the density and breathing mode oscillations. We show that the width of the interparticle interaction potential does not affect the qualitative physics of resonant tunneling dynamics, both at the mean-field and many-body levels. In general, we characterize the impact of the transversal and longitudinal degrees-of-freedom in the many-boson tunneling dynamics at the resonant tunneling scenarios.

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Impact of the transverse direction on the many-body tunneling dynamics in a two-dimensional bosonic Josephson junction

Scientific Reports ◽

10.1038/s41598-020-78173-w ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Anal Bhowmik ◽

Sudip Kumar Haldar ◽

Ofir E. Alon

Keyword(s):

Josephson Junction ◽

Quantum Dynamics ◽

Transverse Direction ◽

General Rule ◽

Time Dependent ◽

Two Dimensional ◽

Many Body ◽

Initial State ◽

The Many ◽

Tunneling Dynamics

AbstractTunneling in a many-body system appears as one of the novel implications of quantum physics, in which particles move in space under an otherwise classically-forbidden potential barrier. Here, we theoretically describe the quantum dynamics of the tunneling phenomenon of a few intricate bosonic clouds in a closed system of a two-dimensional symmetric double-well potential. We examine how the inclusion of the transverse direction, orthogonal to the junction of the double-well, can intervene in the tunneling dynamics of bosonic clouds. We use a well-known many-body numerical method, called the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method. MCTDHB allows one to obtain accurately the time-dependent many-particle wavefunction of the bosons which in principle entails all the information of interest about the system under investigation. We analyze the tunneling dynamics by preparing the initial state of the bosonic clouds in the left well of the double-well either as the ground, longitudinally or transversely excited, or a vortex state. We unravel the detailed mechanism of the tunneling process by analyzing the evolution in time of the survival probability, depletion and fragmentation, and the many-particle position, momentum, and angular-momentum expectation values and their variances. As a general rule, all objects lose coherence while tunneling through the barrier and the states which include transverse excitations do so faster. In particular for the later states, we show that even when the transverse direction is seemingly frozen, prominent many-body dynamics in a two-dimensional bosonic Josephson junction occurs. Implications are briefly discussed.

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Analysis of a Trapped Bose–Einstein Condensate in Terms of Position, Momentum, and Angular-Momentum Variance

Symmetry ◽

10.3390/sym11111344 ◽

2019 ◽

Vol 11 (11) ◽

pp. 1344 ◽

Cited By ~ 6

Author(s):

Ofir E. Alon

Keyword(s):

Angular Momentum ◽

Mean Field ◽

Interaction Model ◽

Einstein Condensate ◽

Two Dimensional ◽

Bose Einstein Condensate ◽

Spatial Dimensions ◽

The Many ◽

Harmonic Interaction ◽

Bose Einstein

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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Entangling Lattice-Trapped Bosons with a Free Impurity: Impact on Stationary and Dynamical Properties

Entropy ◽

10.3390/e23030290 ◽

2021 ◽

Vol 23 (3) ◽

pp. 290

Author(s):

Maxim Pyzh ◽

Kevin Keiler ◽

Simeon I. Mistakidis ◽

Peter Schmelcher

Keyword(s):

Structural Changes ◽

Many Body ◽

Wide Range ◽

Entropy Measures ◽

Particle Level ◽

The Many ◽

The One ◽

Tunneling Dynamics ◽

The Individual ◽

Trapped Bosons

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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Functional mean field expansion for the many-body initial condition problem

Physica A Statistical Mechanics and its Applications ◽

10.1016/0378-4371(89)90407-x ◽

1989 ◽

Vol 159 (3) ◽

pp. 440-458

Author(s):

S. Cruz Barrios ◽

A.F.R. De Toledo Piza

Keyword(s):

Mean Field ◽

Initial Condition ◽

Many Body ◽

Condition Problem ◽

The Many

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Possible weakening of the many-body interactions in the organic quasi-two-dimensional metal α-(BETS)2NH4Hg(SCN)4

Journal of Experimental and Theoretical Physics ◽

10.1134/s1063776109100124 ◽

2009 ◽

Vol 109 (4) ◽

pp. 664-666 ◽

Cited By ~ 4

Author(s):

S. I. Pesotskiĭ ◽

R. B. Lyubovskiĭ ◽

M. V. Kartsovnik ◽

W. Biberacher ◽

N. D. Kushch ◽

...

Keyword(s):

Two Dimensional ◽

Many Body ◽

The Many ◽

Many Body Interactions

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Solvable Model of a Generic Driven Mixture of Trapped Bose–Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles

Entropy ◽

10.3390/e22121342 ◽

2020 ◽

Vol 22 (12) ◽

pp. 1342

Author(s):

Ofir E. Alon

Keyword(s):

Angular Momentum ◽

Infinite Number ◽

Mean Field ◽

Solvable Model ◽

Time Dependent ◽

Angular Momentum Operator ◽

Many Body ◽

The Many ◽

Bose Einstein ◽

Number Of Particles

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of N1 interacting bosons of mass m1 driven by a force of amplitude fL,1 and N2 interacting bosons of mass m2 driven by a force of amplitude fL,2, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are 100% condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces fL,1 and fL,2. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed.

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EFFECTS OF CORE POLARIZATION AND PAIRING CORRELATIONS ON SOME GROUND-STATE PROPERTIES OF DEFORMED ODD-MASS NUCLEI WITHIN THE HIGHER TAMM–DANCOFF APPROACH

International Journal of Modern Physics E ◽

10.1142/s0218301311017594 ◽

2011 ◽

Vol 20 (02) ◽

pp. 252-258 ◽

Cited By ~ 8

Author(s):

LUDOVIC BONNEAU ◽

JULIEN LE BLOAS ◽

PHILIPPE QUENTIN ◽

NIKOLAY MINKOV

Keyword(s):

Ground State ◽

Mean Field ◽

Energy Difference ◽

Pair Type ◽

Many Body ◽

Hartree Fock ◽

Ground State Properties ◽

Pairing Correlations ◽

The Many ◽

The Impact

In self-consistent mean-field approaches, the description of odd-mass nuclei requires to break the time-reversal invariance of the underlying one-body hamiltonian. This induces a polarization of the even-even core to which the odd nucleon is added. To properly describe the pairing correlations (in T = 1 and T = 0 channels) in such nuclei, we implement the particle-number conserving Higher Tamm–Dancoff approximation with a residual δ interaction in each isospin channel by restricting the many-body basis to two-particle–two–hole excitations of pair type (nn, pp and np) on top of the Hartree–Fock solution. We apply this approach to the calculation of two ground-state properties of well-deformed nuclei |Tz| = 1 nuclei around 24 Mg and 48 Cr , namely the isovector odd-even binding-energy difference and the magnetic dipole moment, focusing on the impact of pairing correlations.

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Clusters as surrogate for explicit short-range correlations in relativistic mean-field models

The European Physical Journal Special Topics ◽

10.1140/epjst/e2020-000060-6 ◽

2020 ◽

Vol 229 (22-23) ◽

pp. 3433-3444

Author(s):

Stefan Typel

Keyword(s):

Nuclear Matter ◽

Density Functional ◽

Degrees Of Freedom ◽

Present Model ◽

Mean Field ◽

Theoretical Models ◽

Density Functionals ◽

Many Body ◽

Relativistic Mean Field ◽

Short Range Correlations

AbstractThe formation of clusters at sub-saturation densities in nuclear matter can be seen as a result of many-body correlations. Various theoretical models have been developed to take this effect into account, mostly on a phenomenological level using energy density functionals. These models are constructed in such a way that clusters appear solely in dilute matter and dissolve when the density approaches the nuclear saturation density. At higher densities only nucleons survive as quasi-particles and no explicit correlations between the constituents of nuclear matter are considered. The possible description of correlations with cluster degrees of freedom at supra-saturation densities is explored using the example of a quasi-deuteron in a generalized relativistic density functional. The required change in the density dependence of the cluster mass shift, responsible for describing the cluster dissolution in the present model, is derived for nuclear matter at zero temperature.

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