Double-well Trap Research Articles

Effects of quantum fluctuations on macroscopic quantum tunneling and self-trapping of a BEC in a double-well trap

In this paper, we study the influence of quantum fluctuations (QFs) on the macroscopic quantum tunneling and self-trapping (ST) of a two-component Bose–Einstein condensate in a double-well trap. QFs are described by the Lee–Huang–Yang (LHY) term in the modified Gross–Pitaevskii (GP) equation. Employing the modified GP equation in a scalar approximation, we derive a dimer model using a two-mode approximation. The frequencies of Josephson oscillations and ST conditions under QFs are found analytically and proven by numerical simulations of the modified GP equation. The tunneling and localization phenomena are also investigated for the case of the LHY fluid loaded in a double-well potential.

Faraday-imaging-induced squeezing of a double-well Bose-Einstein condensate

We examine how nondestructive measurements generate spin squeezing in an atomic Bose-Einstein condensate confined in a double-well trap. The condensate in each well is monitored using coherent light beams in a Mach-Zehnder configuration that interacts with the atoms through a quantum nondemolition Hamiltonian. We solve the dynamics of the light-atom system using an exact wave-function approach, in the presence of dephasing noise, which allows us to examine arbitrary interaction times and a general initial state. We find that monitoring the condensate at zero detection current and with identical coherent light beams minimizes the backaction of the measurement on the atoms. In the weak atom-light interaction regime, we find the mean spin direction is relatively unaffected, while the variance of the spins is squeezed along the axis coupled to the light. Additionally, squeezing persists in the presence of tunneling and dephasing noise. For long atom-light interaction time, we equally show our methods can be used to prepare non-Gaussian correlated spin states.

Double-well trap for charged microparticles

We propose a double-well linear Paul trap for particle’s spatial selection according to the charge-to-mass ratio. To perform spatial selection we implemented an experimental setup that permits to detect particles’ positions in the double-well trap from three different view-points: top, front left, and front right. The setup gives an opportunity to monitor the particles’ axial density distribution in real-time. We have shown a strong correlation between axial position of separated localization areas and the DC voltages applied to the rod and end-cap electrodes. We have experimentally determined the critical localization parameters where double-well mode acquires for all the trapped charged microparticles. According to the experimental data and a numerical simulation a upper value of charge-to-mass ratio of the trapped microparticles was estimated.

Creation of double-well potentials in a surface-electrode trap towards a nanofriction model emulator

We demonstrate a microfabricated surface-electrode ion trap that is applicable as a nanofriction emulator and studies of many-body dynamics of interacting systems. The trap enables both single-well and double-well trapping potentials in the radial direction, where the distance between the two potential wells can be adjusted by the applied RF voltage. In the double-well configuration, parallel ion strings can be formed, which is a suitable system for the emulation of the Frenkel–Kontorova (FK) model. We derive the condition under which the trap functions as an FK model emulator. The trap is designed so that the Coulomb interaction between two ion strings becomes significant. We report on the microfabrication process for such downsized trap electrodes and experimental results of single-well and double-well operation with calcium ions. With the trap demonstrated in this work we can create atomically accessible, self-assembled Coulomb systems with a wide tuning range of the corrugation parameter in the FK model. This makes it a promising system for quantum simulations, but also for the study of nanofriction in one and higher dimensional systems.

Spin Squeezing in a Tunneling-Dissipative Bose-Hubbard Dimer

We investigate spin squeezing of a Bose-Einstein condensate in an open symmetrical double-well trap with dissipation in the tunneling process, which can be treated as a tunneling-dissipative Bose-Hubbard dimer. Perturbation technique based on the system is applied. Its shown that more squeezing can be achieved by increasing the tunneling rate and the dissipation.

On a mathematical model for a damped and driven double-well Bose–Einstein condensate

In this paper we consider a two-mode dynamical system as a model for a driven one-dimensional damped Bose–Einstein condensate in a double-well trapping potential. In the case of a constant external driving force the existence and stability of stationary solutions are discussed in relation to the values of the physical parameters. In the case of a time-dependent periodic external driving force the existence of limit cycles is proved, and the amplitude of these limit cycles exhibits a jump phenomenon for critical values of the physical parameters.

Skyrmion-based magnetic traps for ultracold atoms

We show that the stray field generated by isolated magnetic skyrmions can be used to trap ultracold atoms. Specially, ring-shaped and double-well trapping potentials for ultracold atoms can be created by combining the field from two isolated skyrmions. The geometry size, potential barrier, trapping frequency and Majorana loss rate of these magnetic traps can be tuned by the external magnetic field or device configuration. The results here could be useful to develop atomtronics devices by manipulating the magnetic skyrmions with modern spintronics techniques.

Non-linear Dynamics of a Double-Well Bose–Einstein Condensate–Reservoirs System

We investigate the dynamics of a Bose–Einstein condensate (BEC) confined within a symmetric double-well trap out-coupled to reservoirs. Our model is based on the quantum Heisenberg–Langevin approach. Dissipation in the system is induced by the interaction of condensate bosons with the reservoir which determines the Markovian and non-Markovian operational dynamics. These distinct dynamics correspond directly to the choice of function used in the dissipation kernel of the quantum Langevin equation. The main focus of this work is to study non-Markovian dynamics of the system proliferated by the use of Ornstein–Uhlenbeck (OU) memory function. Comparison is made with the Markovian dynamics induced by the use of δ-memory-less function. We have calculated numerically the time evolution of population imbalance and tunneling current of the system and found dissipation destroys the regular pattern of the two-mode BEC phases. Comparison between dissipative models shows significant differences in their dynamics, particularly in the strongly interacting case.

Atom-pair tunneling and quantum phase transition in asymmetry double-well trap in strong-interaction regime**Project supported by the National Natural Science Foundation of China (Grant No. 11075099).

The quantum effect of nonlinear co-tunnelling process, which is dependent on atom-pair tunneling and asymmetry of an double-well trap, is studied by using an asymmetrical extended Bose–Hubbard model. Due to the existence of atom-pair tunneling that describes quantum phenomena of ultracold atom-gas clouds in an asymmetrical double-well trap, the asymmetrical extended Bose–Hubbard model is better than the previous Bose–Hubbard model model by comparing with the experimental data cited from the literature. The dependence of dynamics and quantum phase transition on atom-pair tunneling and asymmetry are investigated. Importantly, it shows that the asymmetry of the extended Bose–Hubbard model, corresponding to the bias between double wells, leads to a number of resonance tunneling processes, which tunneling is renamed conditional resonance tunneling, and corrects the atom-number parity effect by controlling the bias between double wells.

Anyon optics with time-of-flight two-particle interference of double-well-trapped interacting ultracold atoms

The subject of bianyon interference with ultracold atoms is introduced through theoretical investigations pertaining to the second-order momentum correlation maps of two anyons (built upon spinless and spin-1/2 bosonic, as well as spin-1/2 fermionic ultracold atoms) trapped in a double-well optical trap. The two-particle system is modeled according to the recently proposed protocols for emulating an anyonic Hubbard Hamiltonian in ultracold-atom one-dimensional lattices. Because the second-order momentum correlations are mirrored in the time-of-flight second-order interference patterns in space, our findings provide impetus for time-of-flight experimental protocols for detecting anyonic statistics via interferometry measurements of massive particles that broaden the scope of the biphoton interferometry of quantum optics.

Gray and Dark Soliton Behavior and Population Under a Symmetric and Asymmetric Potential Trap

We numerically study the impact of Gaussian barrier height and width on the gray solitons population in a symmetric and asymmetric potential trap. The gray solitons are created in a double-well potential by the density engineering method. Two identical Bose-Einstein condensate fragments are confined and made to collide by switching off the Gaussian barrier in a double-well potential. We find that the gray solitons population can be manipulated by Gaussian barrier height and width. We also study the gray solitons population dependence on the coupling strength. Moreover, we also study the impact of an asymmetry present in the double-well potential. We observe that such an asymmetry always swings the point of collision of the gray solitons. Later, a stationary dark soliton is created by the phase imprinting method and we observe that the initial asymmetry in the double-well potential trap sets the dark soliton into oscillation.

Computational study of cold ions trapped in a double-well potential

ABSTRACTWe report a rigorous computational treatment of quantum dynamics of cold ions in a double-well trap using the time-dependent Schrödinger equation. Our method employs a numerically accurate approach that avoids approximations, such as assumption of weak coupling between the wells; normal mode nature of vibrations; or harmonic approximation for energy spectrum of the double-well system. Our goal is to reproduce, from first principles, the process of energy swaps between the wells observed in the experiments at NIST [Nature 471, 196 (2011)] and Innsbruck [Nature 471, 200 (2011)]. The model parameters and the initial conditions are carefully chosen to mimic experimental conditions. We obtain accurate energies and wave functions of the system numerically, and study the evolution of motional wave packets to provide new insight. This model reproduces experimental results obtained by NIST and Innsbruck in detail. We explain the energy transfer in terms of wave packet dynamics in the asymmetric potential energy well. We also show that, for a localised initial wave packet, this phenomenon can be interpreted using the terms of classical dynamics, such as trajectory of motion governed by the well-known simple principle: the angle of reflection equals the angle of incidence.

Fluctuation damping of isolated, oscillating Bose-Einstein condensates

Experiments on the nonequilibrium dynamics of an isolated Bose-Einstein condensate (BEC) in a magnetic double-well trap exhibit a puzzling divergence: While some show dissipation-free Josephson oscillations, others find strong damping. Such damping in isolated BECs cannot be understood on the level of the coherent Gross-Pitaevskii dynamics. Using the Keldysh functional-integral formalism, we describe the time-dependent system dynamics by means of a multi-mode BEC coupled to fluctuations (single-particle excitations) beyond the Gross-Pitaevskii saddle point. We find that the Josephson oscillations excite an excess of fluctuations when the effective Josephson frequency, $\tilde{\omega}_J$, is in resonance with the effective fluctuation energy, $\tilde{\varepsilon}_m$, where both, $\tilde{\omega}_J$ and $\tilde{\varepsilon}_m$, are strongly renormalized with respect to their noninteracting values. Evaluating and using the model parameters for the respective experiments describes quantitatively the presence or absence of damping.

Dynamical suppression of tunneling and spin switching of a spin-orbit-coupled atom in a double-well trap

We predict wide-band suppression of tunneling of spin-orbit-coupled atoms (or noninteracting Bose-Einstein condensate) in a double-well potential with periodically varying depths of the potential wells. The suppression of tunneling is possible for a single state and for superposition of two states, i.e. for a qbit. By varying spin-orbit coupling one can drastically increase the range of modulation frequencies in which an atom remains localized in one of the potential wells, the effect connected with crossing of energy levels. This range of frequencies is limited because temporal modulation may also excite resonant transitions between lower and upper states in different wells. The resonant transitions enhance tunneling and are accompanied by pseudo-spin switching. Since the frequencies of the resonant transitions are independent of potential modulation depth, in contrast to frequencies at which suppression of tunneling occurs, by varying this depth one can dynamically control both spatial localization and pseudo-spin of the final state.

Emergence of junction dynamics in a strongly interacting Bose mixture

We study the dynamics of a one-dimensional system composed of a bosonic background and one impurity in single- and double-well trapping geometries. In the limit of strong interactions, this system can be modeled by a spin chain where the exchange coefficients are determined by the geometry of the trap. We observe non-trivial dynamics when the repulsion between the impurity and the background is dominant. In this regime, the system exhibits oscillations that resemble the dynamics of a Josephson junction. Furthermore, the double-well geometry allows for an enhancement in the tunneling as compared to the single-well case.

Coherent oscillations in small Fermi-polaron systems

We study the ground state and excitations of a one-dimensional trapped polarized Fermi gas interacting with a single impurity. First, we study the tunnelling dynamics of the impurity through a potential barrier, such as one effectively created by a double-well trap. To this end, we perform an exact diagonalization of the full few-body Hamiltonian and analyze the results in a Local Density Approximation. Off-diagonal and one-particle correlation matrices are studied and are shown to be useful for discerning between different symmetries of the states. Second, we consider a radio-frequency (RF) spectroscopy of our system and the resulting spectral function. These calculations can motivate future experiments, which can provide a further insight into the physics of a Fermi polaron.

Vortex formation and hidden vortices in dipolar Bose–Einstein condensates

We examine vortex formation in dipolar Bose–Einstein condensates (BECs) with rotating double-well (DW) trap potential. For this purpose, we solve a two-dimensional, nonlocal Gross–Pitaevskii equation numerically. We obtain the critical rotation frequency (Ωc) for vortex formation in dipolar BECs for two different species and three different interaction strengths in each case. We also study hidden vortices, which are positioned along the DW potential, for all possible cases.

Crossing Over from Attractive to Repulsive Interactions in a Tunneling Bosonic Josephson Junction.

We explore the interplay between tunneling and interatomic interactions in the dynamics of a bosonic Josephson junction. We tune the scattering length of an atomic ^{39}K Bose-Einstein condensate confined in a double-well trap to investigate regimes inaccessible to other superconducting or superfluid systems. In the limit of small-amplitude oscillations, we study the transition from Rabi to plasma oscillations by crossing over from attractive to repulsive interatomic interactions. We observe a critical slowing down in the oscillation frequency by increasing the strength of an attractive interaction up to the point of a quantum phase transition. With sufficiently large initial oscillation amplitude and repulsive interactions, the system enters the macroscopic quantum self-trapping regime, where we observe coherent undamped oscillations with a self-sustained average imbalance of the relative well population. The exquisite agreement between theory and experiments enables the observation of a broad range of many body coherent dynamical regimes driven by tunable tunneling energy, interactions and external forces, with applications spanning from atomtronics to quantum metrology.

Effective-mass approach to controlling double-well dynamics of atomic Bose-Einstein condensates

The realization of Bose-Einstein condensation in dilute atomic gases opens an exciting way to quantum mechanics and begins a new area of quantum simulation. As a macroscopic quantum object and a many-body bosonic system, the Bose-Einstein condensates can show numerous exotic quantum effects and have naturally attracted great attention. One of the simplest quantum many-body systems to be realized experimentally and studied theoretically is ultra-cold atoms in a double-well potential. This system can exhibit a great variety of quantum interference phenomena such as tunneling oscillation, self-trapping and the entanglement of macroscopic superpositions. Specifically, the double-well potentials built by optical or magnetic fields are easy to change and the many-body interaction between ultra-cold atoms can be changed by the method of Feshbach resonance, enabling the precise quantum control of the double-well dynamics of the condensates. In the present work, we study the dynamics of a condensate in a trapping potential consisting of an unalterable double-well trap and an additional moving optical lattice. If the lattice space is much smaller than the size of the double-well trap, the system can be simplified into a double-well trapped condensate with a tunable effective mass. Using the mean-field factorization assumption, together with a two-mode approximation, we obtain the analytic expressions for the dependence of the tunneling rate and the self-collision strength on the effective mass. The tunneling rate decays and the collision strength grows up with the increase of the effective mass. As a consequence of their different changes, we conclude that the adjustment of the effective mass of the ultra-cold atoms, rather than the changing of the trap barrier or adjusting of the atomic scattering length, is an alternative approach to controlling the double-well dynamics of the condensate. Via numerical simulations of the mean-field dynamical equations with some realistic parameters, we show that a transition between the quantum coherent tunneling and the self-trapping behaviors is experimentally realizable with the mass-control approach. Specifically, we show that the approach is still valid for the case of negative mass. Moreover, we find that the negative-mass case can be used even to stimulate the double-well dynamics of the condensate with a negative atomic scattering length.

Many-body excitations and deexcitations in trapped ultracold bosonic clouds

We employ the MultiConfiguraional Time-Dependent Hartree for Bosons (MCTDHB) method to study excited states of interacting Bose-Einstein condensates confined by harmonic and double-well trap potentials. Two approaches to access excitations, a static and a dynamic one, have been studied and contrasted. In static simulations the low-lying excitations have been computed by utilizing the LR-MCTDHB method - a linear response theory constructed on-top of a static MCTDHB solution. Complimentary, we propose two dynamic protocols that address excitations by propagating the MCTDHB wave-function. In particular, we investigate dipole-like oscillations induced by shifting the origin of the confining potential and breathing-like excitations by quenching frequency of a parabolic part of the trap. To contrast static predictions and dynamic results we have computed time-evolutions and their Fourier transforms of several local and non-local observables. Namely, we study evolution of the $\left< x(t) \right>$, its variance $\operatorname{Var}(x(t))$, and of a local density computed at a selected position. We found out that the variance is the most sensitive and informative quantity - along with excitations it contains information about the de-excitations even in a linear regime of the induced dynamics. The dynamic protocols are found to access the many-body excitations predicted by the static LR-MCTDHB approach.