Coupled Bose Einstein Condensates Research Articles

Stable stripe and vortex solitons in two-dimensional spin-orbit coupled Bose–Einstein condensates

We present a flexible manipulation and control of solitons via Bose–Einstein condensates. In the presence of Rashba spin–orbit coupling and repulsive interactions within a harmonic potential, our investigation reveals the numerical local solutions within the system. By manipulating the strength of repulsive interactions and adjusting spin–orbit coupling while maintaining a zero-frequency rotation, diverse soliton structures emerge within the system. These include plane-wave solitons, two distinct types of stripe solitons, and odd petal solitons with both single and double layers. The stability of these solitons is intricately dependent on the varying strength of spin–orbit coupling. Specifically, stripe solitons can maintain a stable existence within regions characterized by enhanced spin–orbit coupling while petal solitons are unable to sustain a stable existence under similar conditions. When rotational frequency is introduced to the system, solitons undergo a transition from stripe solitons to a vortex array characterized by a sustained rotation. The rotational directions of clockwise and counterclockwise are non-equivalent owing to spin–orbit coupling. As a result, the properties of vortex solitons exhibit significant variation and are capable of maintaining a stable existence in the presence of repulsive interactions.

Anderson localization and quenched induced dynamics of spin orbit coupled Bose–Einstein condensate in a random potential

We consider the localization and dynamical properties of a one dimensional spin orbit coupled Bose–Einstein condensate trapped by a disordered speckle potential. We numerically solve coupled Gross–Pitaevskii equation to obtain ground sate solutions. The effects of spin–orbit coupling and detuning parameter on localization are investigated. It is found that the increase of spin–orbit coupling delocalizes the condensate while the increase of detuning favors localization. After achieving the numerical ground state solutions, we examine the quench induced dynamics of the condensate by the complete cessation of the spin–orbit coupling. We show that at parameters where the ground state is not localized, the dynamics of the system is chaotic.

Compressing the atomic cloud in a matter-wave stripe soliton

We consider an attractive quasi-one dimensional spin-orbit coupled Bose–Einstein condensate (SOC BEC) confined in a periodic potential produced by the combination of linear and nonlinear optical lattices, and study the effects of squeezing a stripe soliton by varying the inter-atomic interaction in the nonlinear lattice. It is observed that the nodes on the soliton arising entirely due to the effect of spin–orbit coupling tend to disappear as we increase the squeezing effect to finally get a stable fundamental soliton. This leads us to conclude that external pressure can reduce the effect of spin–orbit coupling in the SOC BEC and even convert the system to a traditional BEC without spin–orbit coupling. We make use of an information theoretic measure to visualize how does the atomic density distribution in the condensate respond to continual reduction in the spin–orbit coupling effect.

Quantum simulation and Anderson localization in vector rogue waves of Bose-Einstein condensate

We report the existence of vector rogue waves in a coupled Bose-Einstein condensate, trapped in a bichromatic optical lattice, which is an appropriate platform for quantum simulation. Such two-component Bose-Einstein condensate plays a vital role to beget hybrid mixtures and structural transition of nonlinear excitations like rogue waves and solitons. An efficient manipulation of rogue waves is embraced, where we identify the slowing down and stopping of dark rogue wave by lattice engineering. This may nurture quantum memory application and transform the rogue wave mixture immiscible. The existence of Anderson localized rogue wave at the central frustrated lattice site is confirmed by showing the exponential nature and localization length of the condensate. A merging of a dual Anderson rogue waves is manifested in their coherent control. Numerical stability analysis is also carried out for a wide range of trap parameters for experimental viability.

The dynamical stripes in spin–orbit coupled Bose–Einstein condensates with Josephson junctions

The Josephson dynamics of the Bose–Einstein condensation with Raman-induced spin–orbit coupling is investigated. A quasi-1D trap is divided into two reservoirs by an optical barrier. Before the tunneling between the reservoirs is turned on, the system stays in its equilibrium ground state, which displays a rich phase diagram for different spin–orbit coupling parameters and interaction strengths. In this work we focus on the plane wave phase and the stripe phase. Our calculation shows that, when the tunneling is turned on, the plane wave phase evolves into a dynamical stripe phase, that is, the density of the particle changes from uniform to periodically modulated. Basically, this stripe is described by a sine function and the wave length, the amplitude and the initial phase of the function are all varying with time. If the system stays in stripe phase initially, the stripes become “sliding” when the tunneling is turned on, which reflects the running of one of the phases of the wave function.

Emergence of a Spin Microemulsion in Spin-Orbit Coupled Bose-Einstein Condensates.

We report the first numerical prediction of a "spin microemulsion"-a phase with undulating spin domains resembling classical bicontinuous oil-water-surfactant emulsions-in two-dimensional systems of spinor Bose-Einstein condensates with isotropic Rashba spin-orbit coupling. Using field-theoretic numerical simulations, we investigated the melting of a low-temperature stripe phase with supersolid character and find that the stripes lose their superfluidity at elevated temperature and undergo a Kosterlitz-Thouless-like transition into a spin microemulsion. Momentum distribution calculations highlight a thermally broadened occupation of the Rashba circle of low-energy states with macroscopic and isotropic occupation around the ring. We provide a finite-temperature phase diagram that positions the emulsion as an intermediate, structured isotropic phase with residual quantum character before transitioning at higher temperature into a structureless normal fluid.

Multi-stability in cavity QED with spin–orbit coupled Bose–Einstein condensate

Multi-stability in cavity QED with spin–orbit coupled Bose–Einstein condensate

Baseband modulational instability and dynamics of rogue waves in coherently coupled Bose–Einstein condensates

We consider coupled dimensionless Gross-Pitaevskii (GP) equations that describes effective coherently coupled Bose–Einstein condensates (BECs) trapped in external complex potentials. Through a modified similarity transformation, the integrability condition is obtained and the system is reduced to one single integrable autonomous cubic-quintic nonlinear Schrödinger (NLS) equation with self-steepening and self-frequency shift. The baseband modulational instability (MI) for the obtained NLS equation is investigated in details. Through the exact first- and second-order rogue wave solutions with nonlinear chirp of the coupled GP equation, we investigate analytically the propagation dynamics of rogue waves on weakly perturbed continuous wave solutions in the parameter space where the baseband MI exist. Our results show that one can manipulate the motion of matter rogue waves by controlling the external trapping potential. Simulations provide supporting evidence that rogue waves can only emerge in regimes where baseband MI occurs. Our results show how multiplet first- and second-order rogue waves can be generated by varying some solution parameters such as the amplitude parameter.

Stability control in a helicoidal spin–orbit-coupled open Bose–Bose mixture

Abstract In this article, the modulation instability (MI) of open Bose–Bose mixtures with helicoidal spin–orbit coupling (SOC) was studied. Unlike previous spin–orbit (SO)-coupled Bose–Einstein condensate system with helicoidal gauge potential, the purpose of this article to study the input of the helicoidal SOC in the emergence of MI in open Bose–Bose mixtures by taking into account the Lee–Huang–Yang corrections to the coupled Gross–Pitaevskii equations. We present the detailed analyses of system parameters on the characteristics of MI and analytically conclude the parameter conditions for MI occurrence. Our results provide a potential way to manipulate the MI in the helicoidal SO-coupled open Bose–Bose mixtures.

Induced position-dependent spin–orbit coupling in atomic Bose–Einstein condensate

In this paper, we study-induced spin–orbit coupling (SOC) in one-dimensional ultracold quantum gases composed of atoms of different species. One species is subjected to an equal combination of Rashba and Dresselhaus SOC generated by Raman transition. The two species interact with each other through spin-independent and spin-exchange contact interactions. The spin-exchange interaction introduces a locking pattern of the momentum and spin degrees of freedom for the species without direct SOC. For small spin-independent interactions, the two species overlap and the induced SOC is effective. For large spin-independent interactions, however, the two species keep separate from each other and the induced SOC is negligible. We propose to generate inhomogeneous SOC by exploiting density engineering technique applied to the directly spin–orbit coupled Bose–Einstein condensate. When the effective potential is of Gaussian type, the single-particle eigenenergies and eigenstates are calculated by exact diagonalization method. For general cases, mean-field ground states are obtained by numerically searching for the minimum of energy functional. With the density engineering technique, it is possible to produce hybrid structures of plane wave, stripe and/or zero-momentum phases.

Metastable supersolid in spin-orbit-coupled Bose-Einstein condensates

Supersolid is a special state of matter with both superfluid properties and spontaneous modulation of particle density. In this paper, we focus on the supersolid stripe phase realized in a spin-orbit coupled Bose-Einstein condensate and explore the properties of a class of metastable supersolids. In particular, we study a one-dimensional supersolid whose characteristic wave number $k$ (magnitude of wave vector) deviates from $k_{m}$, i.e., the one at ground state. In other words, the period of density modulation is shorter or longer than the one at ground state. We find that this class of supersolids can still be stable if their wave numbers fall in the range $k_{c1}<k<k_{c2}$, with two thresholds $k_{c1}$ and $k_{c2}$. Stripes with $k$ outside this range suffer from dynamical instability with complex Bogoliubov excitation spectrum at long wavelength. Experimentally, these stripes with $k$ away from $k_m$ are accessible by exciting the longitudinal spin dipole mode, resulting in temporal oscillation of stripe period as well as $k$. Within the mean-field Gross-Pitaevskii theory, we numerically confirm that for a large enough amplitude of spin dipole oscillation, the stripe states become unstable through breaking periodicity, in qualitative agreement with the existence of thresholds of $k$ for stable stripes. Our work extends the concept of supersolid and uncovers a new class of metastable supersolids to explore.

Bright–dark Peregrine solutions in helicoidal spin–orbit coupled Bose–Einstein condensates

Vector Gross–Pitaevskii system in helicoidal spin–orbit coupled Bose–Einstein condensates can be reduced into vector nonlinear Schrödinger system. Employing the nonrecursive Darboux method, we find bright–dark Peregrine solutions, such as first-order and second-order vector Peregrine solutions, including vector Peregrine “three sisters” solutions. These results will provide a deeper understanding of nonlinear wave phenomena in helicoidal spin–orbit coupled Bose–Einstein condensates.

Anharmonicity-induced phase transition of spin–orbit coupled Bose–Einstein condensates

In the mean-field framework, using variational analysis and numerical simulation, we investigate the effect of anharmonic trap and atomic interaction on the ground-state phases of spin-orbit (SO) coupled Bose–Einstein condensates (BECs) in the harmonic plus quartic potential. Then, the Gaussian wave function is selected to predict the analytical conditions of the phase transition boundary of the SO coupled BECs by using the variational method. We found that the anharmonicity of the external potential induces the SO coupled BECs to undergo a phase transition between the zero-momentum phase and plane-wave phase, which is more pronounced in the cases of weak harmonic potential or strong interspecies interaction. Since the potential energy of the system modified by anharmonicity competes with other energies of the system, the anharmonicity changes the critical SO coupling strength and Raman coupling strength when the phase transition occurs. At the same time, the critical anharmonic coefficients are also affected by interspecies interaction and harmonic potential. Finally, the correctness of the theoretical results is verified by numerical simulation of the Gross-Pitaevskii equation.

Dynamics of spin-tensor-momentum coupled Bose-Einstein condensates

We investigate the dynamics of the plane wave state in one-dimensional spin-tensor-momentum coupled Bose-Einstein condensate. By using the Gaussian variational approximation, we first derive the equations of motion for the variational parameters, including the center-of-mass coordinate, momentum, amplitude, width, chirp, and relative phase. These variational parameters are coupled together nonlinearly by the spin-tensor-momentum coupling, Raman coupling, and the spin-dependent atomic interaction. By minimizing the energy with respect to the variational parameters, we find that the ground state is a biaxial nematic state, the momentum of the ground state decreases monotonically with the increase of the strength of the Raman coupling, and the parity of real part of the ground-state wave function is opposite to that of the imaginary part. The linear stability analysis shows that the ground state is dynamically stable under a perturbation, and exhibits three different oscillation excitation modes, the frequencies of which are related to the strength of the Raman coupling, the aspect ratio of the harmonic trap, and the strength of the atomic interaction. By solving the equations of motion for the variational parameters, we find that the system displays periodical oscillation in the dynamical evolution. These variational results are also confirmed by the direct numerical simulations of the Gross-Pitaevskii equations, and these findings reveal the unique properties given by the spin-tensor-momentum coupling.

Adiabatic elimination theory of multi-level system in spin-orbit coupled Bose-Einstein condensate

In quantum optics, adiabatic elimination simplifies multi-level quantum system by eliminating the fast oscillatory degree of freedom and preserving the slow-varying dynamics, thus obtaining an efficient description of the system. Adiabatic elimination has important applications in quantum simulation and quantum precision measurement. For example, spin-orbit coupling has been realized in ultracold atoms by using three-level Raman coupling and adiabatic elimination. In this paper, we investigate the theoretical method and generalize the adiabatic elimination in three-level non-Hermitian systems and multi-level systems on the basis of standard elimination scheme. These can provide theoretical guidance for realizing the interdiscipline of non-Hermitian physics and spin-orbit coupling effects and their potential applications. We mainly discuss the influences of dissipative effect on the population dynamics of the system, the validity and accuracy of the adiabatic elimination theory under different parameters for both non-Hermitian and two types of five-level systems. Specifically, the dynamics satisfying the large detuning condition gives very accurate results for quite a long evolution time with the adiabatic elimination theory, but when the two-photon detuning &lt;i&gt;δ&lt;/i&gt; and the Rabi frequency &lt;inline-formula&gt;&lt;tex-math id="Z-20231017181120"&gt;\begin{document}$\varOmega $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20231052_Z-20231017181120.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20231052_Z-20231017181120.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; gradually increase, leading to the violation of the large detuning condition &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ \varOmega,\gamma, \delta \ll \Delta$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20231052_M1.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20231052_M1.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;, the effective two-level model can no longer describe the fast-varying dynamics of the system even in a short evolution time. Thus the choice of system parameters affects the effectiveness of adiabatic elimination of the excited levels. In a non-Hermitian system, the population in the ground state oscillates with gain periodically at the beginning, while that in the ground state oscillates with loss and decreases with time, with the total population decreasing with oscillation. For long-time evolution the gain in the system causes the population to diverge, and the adiabatic elimination of the effective two-energy level system describes this behavior accurately. The effect of the non-Hermitian parameters on the dynamics of the system in the resonance case is manifested in the case that the total population remains conserved, while the total population tends to diverge for finite two-photon detuning. We find that with the increase of detuning, the divergence appears earlier and the total number of particles can be kept constant by choosing the ratio of gain to loss appropriately. This study provides a theoretical basis for state preparation and dynamical manipulation in dissipative multi-energy quantum systems.

Quench dynamics of a spin-orbital coupled Bose-Einstein condensate with nonlinear interactions

In this work, we study the non-equilibrium quench dynamics from the superfluid stripe phase to the supersolid phase of a two dimensional spin-orbital coupled interacting Bose-Einstein condensate in the presence of a one dimensional optical lattice. The quench protocol here is constructed through varying the lattice depth linearly with the evolution time. By using the time-dependent Gutzwiller method, various physical quantities, such as the vortex number and the overlap of wave-function, have been investigated with respect to the quench time. Through analyzing the dynamical behavior of the above physical quantities, we find out the transition time of the quench procedure, which captures the freeze out time indicating the moment that the system catches the quench speed beginning to evolve quickly. Before the transition time, the dynamics is frozen and the state of the system cannot follow the changes in the Hamiltonian. While passing the transition time, we find that there are significant alterations to both the vortex number and the wave-function. At the transition time, on one hand the vortex number abruptly increases from zero; on the other hand the overlap of wave-function departures from 1 shortly. These signatures indicate that the system evolves rapidly when passing the transition time. Furthermore, we also find that due to the presence of spin-orbital coupling, the spin texture represents a periodic magnetic structure accompanying with the emergence of the supersolid dynamically. It is shown that during the quench procedure, the density distribution of the system are always accompanied with the spatial structure of spin texture, i.e., the central position of topological spin skyrmion (antiskyrmion) corresponding to the minimum position of the density distribution. The topological charge of the above spin structures also shows interesting dynamical properties. We find that the quantized topological charge appears with the emergence of the supersolid dynamically.

Quantum droplets with topological textures in a dipolar condensate

We investigate a spin–orbit coupled Bose–Einstein condensate containing both dipolar and non-dipolar components. Combined with Rashba spin–orbit coupling, the competition between contact and dipolar interaction reveals four distinctive exotic phases: droplet lattice phase, stripe phase, oblique stripe phase, and labyrinthine stripe phase. In particular, we adopt a condensate order parameter ansatz to characterize the superstripe phase in a harmonic trap through minimizing the analytical total energy. Furthermore, we find that the energy analysis of the dipolar condensate in the trap uncovers a higher order transition from lattice to stripe phases when contact interaction increases. Our results demonstrate the possibility for physicists to realize a wealth of controllable configurations in spin–orbit coupled dipolar condensates, including droplet lattice with topology and superstripe adjusted by changing the strength of contact and dipolar interactions. The topological phases we predict in this work can be realized by using state-of-the-art techniques in ultracold atomic experiments of chromium, erbium, or dysprosium condensates.

Excitation of chaotic atomic population oscillations in a spin-orbit coupled Bose-Einstein condensate with a square-wave driving

In this paper, we have investigated the excitation of chaotic atomic population oscillations in a spin-orbit (SO) coupled Bose-Einstein condensate (BEC). Unlike previous SOC system with monochrome and bichromatic driving, the present system reveals the chaotic excitation induced by the initial condition in the nondissipative regime and by the driving strength in the dissipative regime under the action of a square-wave driving. The damping-dependent chaotic parameter regions and the modulation of atomic population oscillations by the square-wave driving are studied. The existence of chaos is confirmed by computing the corresponding largest Lyapunov exponents. The results could be significant in the quantum transport of the SO coupled cold-atom system.

Tunneling dynamics of spin-orbit coupled BECs in a one-dimensional accelerating optical lattice

We theoretically investigate the energy band structure, nonlinear Landau–Zener tunneling dynamics and tunneling probability of spin-orbit coupled Bose–Einstein condensates in a one-dimensional accelerating optical lattice by using mean-field and two-mode approximation. The critical condition for the appearance of the loop structure is obtained numerically in parameter planes. When the intraspecies atomic interaction is less than the interspecies atomic interaction, the loop only appears in the lower band. In this case, Raman coupling inhibits the appearance of loop, while spin-orbit coupling (SOC) promotes the appearance of loop. If the intraspecies atomic interaction is larger than interspecies atomic interaction, the loop can appear in either the upper band or the lower band. In this case, Raman coupling promotes the loop appearing in the lower band, while SOC suppresses the loop appearing in upper band. Interestingly, when the interspecies atomic interaction is equal to the intraspecies atomic interaction, there is a critical atomic intercation value determined by the optical lattice depth, only when the intraspecies atomic interaction is greater than the critical value, the loop will occur only in lower band. Especially, the emergence of the loop structure destroys the Bloch oscillation of the system and results in the nonlinear Landau–Zener tunneling of the system. Furthermore, the Landau–Zener tunneling probability of the system is calculated, and it is found that the nonlinear Landau–Zener dynamics and the tunneling probability can be manipulated by SOC and Raman coupling.

Harnessing center-of-mass excitations in quantum metrology

In quantum metrology, one typically creates correlations among atoms or photons to enhance measurement precision. Here, we show how one can use other excitations to perform quantum-enhanced measurements on the example of center-of-mass excitations of a spin-orbit coupled Bose-Einstein condensate and a Coulomb crystal. We also present a method to simulate a homodyne detection of cent er-of-mass excitations in these systems, which is required for optimal estimation.