We study the full-fledged microscopic dynamics of two interacting, ultracold bosons in a one- dimensional double-well potential, through the numerically exact diagonalization of the many-body Hamiltonian. With the particles initially prepared in the left well, we increase the width of the right well in subsequent trap realizations and witness how the tunneling oscillations evolve into particle loss. In this closed system, we analyze the spectral signatures of single- and two-particle tunneling for the entire range of repulsive interactions. We conclude that for comparable widths of the two wells, pair-wise tunneling of the bosons may be realized for specific system parameters. In contrast, the decay process (corresponding to a broad right well) is dominated by uncorrelated single-particle decay.
We study the tunneling of a small ensemble of strongly repulsive bosons in a one-dimensional triple-well potential. The usual treatment within the single-band approximation suggests suppression of tunneling in the strong interaction regime. However, we show that several windows of enhanced tunneling are opened in this regime. This enhanced tunneling results from higher band contributions, and has the character of interband tunneling. It can give rise to various tunneling processes, such as single-boson tunneling and two-boson correlated tunneling of the ensemble of bosons, and is robust agains…
We discuss the relaxation dynamics for a bosonic tunneling junction with two modes in the central potential well. We use a master equation description for ultracold bosons tunneling in the presence of noise and incoherent coupling processes into the two central modes. Whilst we cannot quantitatively reproduce the experimental data of the setup reported in [Phys. Rev. Lett. {\bf 115}, 050601 (2015)], we find a reasonable qualitative agreement of the refilling process of the initially depleted central site. Our results may pave the way for the control of bosonic tunneling junctions by the simult…
The level splitting formula of an asymmetric double well potential is calculated taking into account the multi-instanton contributions (dilute gas approximation). Results can be related with known semiclassical ones obtained with a truncated hamiltonian, and the symmetric case is easily recovered.
We propose an asymmetric double quantum well structure with a common continuum and investigate the effect of resonant tunneling on the control of coherent electron population transfer between the two quantum wells. By numerically solving the motion equations of element moments, the almost complete electron population transfer from initial subband to the target subband could be realized due to the constructive interference via flexibly adjusting the structure parameters.
We propose a scheme for precise control of tunneling dynamics of dipolar bosons in shaken triple-well potentials. In the high-frequency regimes and under the resonance conditions, we have analytically and numerically demonstrated that we can transport a priori prescribed number of dipolar bosons along different pathways and different directions by adjusting the driving parameters. These results extend the previous many-body selective coherent destruction of tunneling (CDT) schemes for nondipolar bosons in double-well potentials[Phys. Rev. Lett. 103, 133002 (2009); Phys. Rev. A 86, 044102 (2012…
We show that multi-orbital and density-induced tunneling have a significant impact on the phase diagram of bosonic atoms in optical lattices. Off-site interactions lead to density-induced hopping, the so-called bond-charge interactions, which can be identified with an effective tunneling potential and can reach the same order of magnitude as conventional tunneling. In addition, interaction-induced higher-band processes also give rise to strongly modified tunneling, on-site and bond-charge interactions. We derive an extended occupation-dependent Hubbard model with multi-orbitally renormalized p…
Despite quantum tunneling has been studied since the advent of quantum mechanics, the literature appears to contain no simple (textbook) formula for tunneling in generic asymmetric double-well potentials. In the regime of strong localization, we derive an succinct analytical formula based on the WKB semi-classical approach. Two different examples of asymmetric potentials are discussed: when the two localized levels are degenerate or not. For the first case, we also discuss a time-dependent problem showing quantum Zeno effect.
We have studied dynamical properties and quantum tunneling in asymmetric double-well (DW) systems, by solving Schrödinger equation with the use of two kinds of spectral methods for initially squeezed Gaussian wavepackets. Time dependences of wavefunction, averages of position and momentum, the auto-correlation function, an uncertainty product and the tunneling probability have been calculated. Our calculations have shown that (i) the tunneling probability is considerably reduced by a potential asymmetry $ΔU$, (ii) a resonant tunneling with $|ΔU| \simeq κ\:\hbar ω$ is realized for motion starti…
An asymmetric double-well potential is considered, assuming that the minima of the wells are quadratic with a frequency $ω$ and the difference of the minima is close to a multiple of $\hbar ω$. A WKB wave function is constructed on both sides of the local maximum between the wells, by matching the WKB function to the exact wave functions near the classical turning points. The continuities of the wave function and its first derivative at the local maximum then give the energy-level splitting formula, which not only reproduces the instanton result for a symmetric potential, but also elucidates t…
We theoretically investigate the generation of microscopic atomic NOON states, corresponding to the coherent |N,0> + |0,N> superposition with N ~ 5 particles, via collective tunneling of interacting ultracold bosonic atoms within a symmetric double-well potential in the self-trapping regime. We show that a periodic driving of the double well with suitably tuned amplitude and frequency parameters allows one to substantially boost this tunneling process without altering its collective character. The time scale to generate the NOON superposition, which corresponds to half the tunneling time and w…
We investigate the mechanism in the tunneling dynamics of open ultracold few-boson systems by numerically solving the time-dependent few-boson Schrödinger equation exactly. By starting from a weakly repulsive, initially coherent two-boson system we demonstrate that the decay dynamics incorporate fragmentation. The wavefunction of the tunneling state exhibits a pronounced dynamically-stable pattern which we explain by an analytical model. By studying more bosons and stronger interactions we arrive to the conclusion that the decay by tunneling is not a coherent process and exhibits a wealth of p…
Using a simple model for nonlinear Landau-Zener tunneling between two energy bands of a Bose-Einstein condensate in a periodic potential, we find that the tunneling rates for the two directions of tunneling are not the same. Tunneling from the ground state to the excited state is enhanced by the nonlinearity, whereas in the opposite direction it is suppressed. These findings are confirmed by numerical simulations of the condensate dynamics. Measuring the tunneling rates for a condensate of rubidium atoms in an optical lattice, we have found experimental evidence for this asymmetry.
We study the interplay between the dynamics of a Bose-Einstein condensate in a double-well potential and that of an optical cavity mode. The cavity field is superimposed to the double-well potential and affects the atomic tunneling processes. The cavity field is driven by a laser red detuned from the bare cavity resonance; the dynamically changing spatial distribution of the atoms can shift the cavity in and out of resonance. At resonance the photon number is hugely enhanced and the atomic tunneling becomes amplified. The Josephson junction equations are revisited and the phase diagram is calc…
An asymmetric double quantum wells (QWs) structure with resonant tunneling is suggested to achieve high efficient four wave mixing (FWM). We analytically demonstrate that the resonant tunneling can induce high efficient mixing wave in such a semiconductor structure with a low light pump wave. In particular, the FWM conversion efficiency can be enhanced dramatically in the vicinity of the center frequency. This interesting scheme may be used to generate coherent long-wavelength radiation in solid-state system.
Inter-site dipolar interactions induce, even in absence of disorder, an intriguing non-ergodic dynamics for dipolar bosons in an optical lattice. We show that the inherent dipole-induced density-dependent tunneling, typically neglected, plays a crucial role in this dynamics. For shallow-enough lattices, the delocalization stemming from the interaction-induced hopping overcomes the localization induced by inter-site interactions. As a result, in stark contrast to the more studied case of hard-core bosons, delocalization is counter-intuitively strengthen when the dipolar strength increases. Furt…
A Bose-Hubbard Hamiltonian, modeling cold bosons in an optical lattice, is used to simulate the dynamics of interacting open quantum systems as subsystems a larger closed system, avoiding complications like the introduction of baths, complex absorbing potentials or absorbing boundaries. The numerically exact unitary dynamics is compared with effective descriptions of the subsystems based on non-Hermitian Hamiltonians or Lindblad master equations. The validity of popular models with constant decay rates is explicitly analyzed for decaying single and double wells. In addition we present a discre…
An optical realization of the tunneling dynamics of two interacting bosons in a double-well potential, based on light transport in a four-core microstructured fiber, is proposed. The optical setting enables to visualize in a purely classical system the entire crossover from Rabi oscillations to correlated pair tunneling and to tunneling of a fragmented pair in the fermionization limit.
We report the first experimental observation of the resonance-assisted dynamical tunneling (RADT) in the inter-mode interaction in an asymmetric-deformed microcavity. A selection rule for strong inter-mode coupling induced by RADT was observed on angular mode numbers as predicted by the RADT theory. In addition, the coupling strength was measured to be proportional to the square of the phase-space area associated with the nonlinear resonance involved in RADT. The proportionality constant was found to depend only on the nonlinear resonance, supporting the semiclassical nature of RADT.
A new route to coherent destruction of tunneling is established by considering a monochromatic fast modulation of the self-interaction strength of a many-boson system. The modulation can be tuned such that only an arbitrarily, a priori prescribed number of particles are allowed to tunnel. The associated tunneling dynamics is sensitive to the odd or even nature of the number of bosons.
Tunneling 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 mul…
An asymmetric double-well potential is considered, assuming that the wells are parabolic around the minima. The WKB wave function of a given energy is constructed inside the barrier between the wells. By matching the WKB function to the exact wave functions of the parabolic wells on both sides of the barrier, for two almost degenerate states, we find a quantization condition for the energy levels which reproduces the known energy splitting formula between the two states. For the other low-lying non-degenerate states, we show that the eigenfunction should be primarily localized in one of the we…
The interaction blockade phenomenon isolates the motion of a single quantum particle within a multi-particle system, in particular for coherent oscillations in and out of a region affected by the blockade mechanism. For identical quantum particles with Bose statistics, the presence of the other particles is still felt by a bosonic stimulation factor $\sqrt{N}$ that speeds up the coherent oscillations, where $N$ is the number of bosons. Here we propose an experiment to observe this enhancement factor with a small number of bosonic atoms. The proposed protocol realises an asymmetric double well …
We investigate quantum tunneling of two repulsive bosons in a triple-well potential subject to a high-frequency driving field. By means of the multiple-time-scale asymptotic analysis, we evidence a far-resonant strongly-interacting regime in which the selected coherent destruction of tunneling can occur between the paired states and unpaired states, and the dominant tunneling of the paired states is a second order process. Two Floquet quasienergy bands of the both kinds of states are given analytically, where a fine structure up to the second order corrections is displayed. The analytical resu…
Using the time-dependent density matrix renormalization group (TDMRG) we theoretically study the collision of a one-dimensional gas of interacting bosons with an impurity trapped in a shallow box potential. We study the dynamic response of both the impurity and the bosonic gas and find an approximate independence of the sign of the interaction (attractive or repulsive) between the impurity and the bosons. This sign-independence breaks down when the interaction energy is of the same order as the box potential depth, leading to resonant pair tunneling. Our predictions can be tested using contemp…
We theoretically analyze the phase diagram of a quantum gas of bosons that interact via repulsive dipolar interactions. The bosons are tightly confined by an optical lattice in a quasi one-dimensional geometry. In the single-band approximation, their dynamics is described by an extended Bose-Hubbard model where the relevant contributions of the dipolar interactions consist of density-density repulsion and correlated tunneling terms. We evaluate the phase diagram for unit density using numerical techniques based on the density-matrix renormalization group algorithm. Our results predict that cor…
We investigate few-boson tunneling in a one-dimensional double well, covering the full crossover from weak interactions to the fermionization limit of strong correlations. Based on exact quantum-dynamical calculations, it is found that the tunneling dynamics of two atoms evolves from Rabi oscillations to correlated pair tunneling as we increase the interaction strength. Near the fermionization limit, fragmented-pair tunneling is observed and analyzed in terms of the population imbalance and two-body correlations. For more atoms, the tunneling dynamics near fermionization is shown to be sensiti…
The non-equilibrium dynamics of small boson ensembles in a one-dimensional optical lattice is explored upon a sudden quench of an additional harmonic trap from strong to weak confinement. We find that the competition between the initial localization and the repulsive interaction leads to a resonant response of the system for intermediate quench amplitudes, corresponding to avoided crossings in the many-body eigenspectrum with varying final trap frequency. In particular, we show that these avoided crossings can be utilized to prepare the system in a desired state. The dynamical response is show…
We study a set of $L$ spatial bosonic modes localized on a graph $Γ.$ The particles are allowed to tunnel from vertex to vertex by hopping along the edges of $Γ.$ We analyze how, in the exact many-body eigenstates of the system i.e., Bose-Einstein condensates over single-particle eigenfunctions, the bi-partite quantum entanglement of a lattice vertex with respect to the rest of the graph depends on the topology of $Γ.$
We show that the probability distribution of the stationary state of a dissipative ac-driven two-level system exhibits discontinuities, i.e. jumps, for parameters at which coherent destruction of tunneling takes place. These discontinuities can be observed as jumps in the emission of the Mollow triplet. The jumps are the consequence of discontinuities in the transition rates, which we calculate numerically and analytically based on the secular Floquet-Redfield formalism.
Reflection of two strongly interacting bosons with long-rage interaction hopping on a one-dimensional lattice scattered off by a potential step is theoretically investigated in the framework of the extended Hubbard model. The analysis shows that, in the presence of unbalanced on-site and nearest-neighbor site interaction, two strongly correlated bosons forming a bound particle state can penetrate a high barrier, despite the single particle can not. Such a phenomenon is analogous to one-dimensional Klein tunneling of a relativistic massive Dirac particle across a potential step.
We propose a scheme to dynamically create a supersolid state in an optical lattice, using an attractive mixture of mass-imbalanced bosons. Starting from a "molecular" quantum crystal, supersolidity is induced dynamically as an out-of-equilibrium state. When neighboring molecular wavefunctions overlap, both bosonic species simultaneously exhibit quasi-condensation and long-range solid order, which is stabilized by their mass imbalance. Supersolidity appears in a perfect one-dimensional crystal, without the requirement of doping. Our model can be realized in present experiments with bosonic mixt…
The dynamics of the population imbalance of bosons in a double-well potential is investigated from the point of view of many-body quantum mechanics in the framework of the two-mode model. For small initial population imbalances, coherent superpositions of almost equally spaced energy eigenstates lead to Josephson oscillations. The suppression of tunneling at population imbalance beyond a critical value is related to a high concentration of initial state population in the region of the energy spectrum with quasi-degenerate doublets resulting in imbalance oscillations with a very small amplitude…
We investigate quantum tunneling in smooth symmetric and asymmetric double-well potentials. Exact solutions for the ground and first excited states are used to study the dynamics. We introduce Wigner's quasi-probability distribution function to highlight and visualize the non-classical nature of spatial correlations arising in tunneling.
We study the tunneling dynamics of bosonic and fermionic Tonks-Girardeau gases from a hard wall trap, in which one of the walls is substituted by a delta potential. Using the Fermi-Bose map, the decay of the probability to remain in the trap is studied as a function of both the number of particles and the intensity of the end-cap delta laser. The fermionic gas is shown to be a good candidate to study deviations of the non-exponential decay of the single-particle type, whereas for the bosonic case a novel regime of non-exponential decay appears due to the contributions of different resonances o…
A local impurity usually only strongly affects few single-particle energy levels, thus cannot induce a quantum phase transition (QPT), or any macroscopic quantum phenomena in a many-body system within the Hermitian regime. However, it may happen for a non-Hermitian impurity. We investigate the many-body ground state property of a one-dimensional tight-binding ring with an embedded single asymmetrical dimer based on exact solutions. We introduce the concept of semi-localization state to describe a new quantum phase, which is a crossover from extended to localized state. The peculiar feature is …
We consider an extended Bose-Hubbard model that includes pair-correlated tunneling. We demonstrate that a minimal four-mode implementation of this model exhibits a pair-correlated regime in addition to Mott insulator and superfluid regimes. We propose a low complexity variational subspace for the ground state of the system in the pair-correlated regime, which we find to be numerically exact in pure pair-tunneling limit. Additionally, we propose a parameter-free high fidelity model wave function that qualitatively captures the features of the ground state in the pair-correlated regime. Although…
Stabilizing correlated pair tunneling of spin-orbit-coupled bosons in a non-Hermitian driven double well
Key Laboratory of Low-dimensional Quantum Structures and Quantum Control of Ministry of Education, Key Laboratory for Matter Microstructure and Function of Hunan Province, and Hunan Research Center of the Basic Discipline for Quantum Effects and Quantum Technologies, School of Physics and Electronics, Hunan Normal University（湖南师范大学物理与电子学院）；School of Physics and Electronic Information Engineering, Ningxia Normal University（宁夏师范大学物理与电子信息工程学院）
We derive families of optimal and near-optimal probe states for quantum estimation of the coupling constants of a general two-mode number-conserving bosonic Hamiltonian describing one-body and two-body dynamics. We find that the optimal states for estimating the dephasing of the modes, the self-interaction strength, and the contact interaction strength are related to the NOON states, whereas the optimal states for estimation of the intermode single particle tunneling amplitude are superpositions of antipodal SU(2) coherent states. For estimation of the amplitude of pair tunneling and the ampli…
Efficient simulation of quantum mechanical problems can be performed in a quantum computer where the interactions of qubits lead to the realization of various problems possessing quantum nature. Spin-Boson Model (SBM) is one of the striking models in quantum physics that enables to describe the dynamics of most of the two-level quantum systems through the bath of harmonic oscillators. Here we simulate the SBM and illustrate its applications in a biological system by designing appropriate quantum circuits for the Hamiltonian of photosynthetic reaction centers in IBM's 5-qubit quantum computer. …
We study the dynamics of a particle tunneling between the ground states of a symmetric double potential well system, in the presence of simultaneous diagonal and non-diagonal couplings to an Ohmic oscillator bath. We use the noninteracting-blip approximation to investigate coherence effects across a wide range of system-environment coupling strengths at physiological temperatures. We show how the presence of a non-diagonal coupling mechanism significantly alters the dynamics of the tunneling particle, producing coherent oscillations despite strong thermal fluctuations in the environment. Fluct…
The perfect quenching of spin tunneling first predicted for a model with biaxial symmetry, and recently observed in the magnetic molecule Fe_8, is further studied using the discrete phase integral (or Wentzel-Kramers-Brillouin) method. The analysis of the previous paper is extended to the case where the magnetic field has both hard and easy components, so that the Hamiltonian has no obvious symmetry. Herring's formula is now inapplicable, so the problem is solved by finding the wavefunction and using connection formulas at every turning point. A general formula for the energy surface in the vi…
We present exact expressions for the quantum sloshing of Bose-Einstein condensates in a tilted two-well potential. Tunneling is suppressed by a small potential difference between wells, or tilt. However, tunneling resonances occur for critical values of the tilt when the barrier is high. At resonance, tunneling times on the order of 10-100 ms are possible. Furthermore, such tilted resonances lead to a dynamical scheme for creating few-body NOON-like macroscopic superposition states which are protected by the many body wavefunction against potential fluctuations.
