Spinor Bose Gas Research Articles

Imaging spinor Bose gases using off-axis holography

Imaging spinor Bose gases using off-axis holography

Dynamic stability in spinor Bose gases in moiré lattices with square and hexagonal symmetries

A broad range of phenomena in correlated electrons traveling in moir\'e lattices has emerged in both scenarios, experiments and theory. In this paper we report the observation of a dynamic stability that arises in an analogous system to that of electrons, a weakly interacting spinor Bose gas of ultracold $^{23}\mathrm{Na}$ atoms lying in a single layer having a moir\'e pattern with square and hexagonal symmetries. Our paper is based on the dynamical description of two magnetic domains represented by two hyperfine spin components of a Bose condensate initially localized in the left and right halves of a moir\'e lattice defined by a specific angle $\ensuremath{\theta}$ plus a harmonic confinement. To demonstrate the persistence of such an initial condition under the competence of the moir\'e pattern and harmonic confinements we studied both single noninteracting and double-domain interacting cases. We solve the time dependent Gross-Pitaevskii equations, and track the time evolution of several observables on each half as a function of the twisting angle. In the case of square moir\'e lattices we found a dynamic stability for angles larger than a special one ${\ensuremath{\theta}}_{s}$, except for the Pythagorean angles. The value of such an angle depends on the existence of a harmonic trap when interactions are absent, while this dependence is negligible for the interacting case. Hexagonal moir\'e lattices exhibit the dynamic stability starting from a certain angle that also depends on the harmonic confinement for the noninteracting case.

Separation of quadrupole, spin, and charge across the magnetic phases of a one-dimensional interacting spin-1 gas

We study the low-energy collective properties of a one-dimensional spin-1 Bose gas using bosonization. After giving an overview of the technique, emphasizing the physical aspects, we apply it to the $S=1$ Bose-Hubbard Hamiltonian and find a separation of the quadrupole-spin-charge sectors, confirmed by time--matrix-product states (time-MPS) numerical simulations. Additionally, through the single-particle spectrum, we show the existence of the superfluid--Mott-insulator transition and the point at which the physics are described by a Heisenberg-like Hamiltonian. The magnetic phase diagrams are found for both the superfluid and insulating regimes; the latter is determined by decomposing the complete Heisenberg bilinear-biquadratic Hamiltonian, which describes the Mott insulator, into simpler, effective Hamiltonians. This allows us to keep our methods flexible and transferable to other interesting interacting condensed matter systems.

Synthetic U(1) gauge invariance in a spin-1 Bose gas

Recent experimental realizations of the lattice Schwinger model [Nature 587, 392 (2020) and Science 367, 1128 (2020)] open a door for quantum simulation of elementary particles and their interactions using ultracold atoms, in which the matter and gauge fields are constrained by a local U(1) gauge invariance known as the Gauss's law. Stimulated by such exciting progress, we propose a new scenario in simulating the lattice Schwinger model in a spin-1 Bose-Einstein condensate. It is shown that our model naturally contains an interaction of the matter fields which respects the U(1) gauge symmetry but has no counterpart in the conventional Schwinger model. In addition to the Z2-ordered phase identified in the previous work, this additional interaction leads to a new Z3-ordered phase. We map out a rich phase diagram and identify that the continuous phase transitions from the disordered to the Z2-ordered and the Z3-ordered phases belong to the Ising and the 3-state Potts universality classes, respectively. Furthermore, the two ordered phases each possess a set of quantum scars which give rise to anomalous quantum dynamics when quenched to a special point in the phase diagram. Our proposal provides a novel platform for extracting emergent physics in cold-atom-based quantum simulators with gauge symmetries.

Condensation and thermalization of an easy-plane ferromagnet in a spinor Bose gas

The extensive control of spin makes spintronics a promising candidate for future scalable quantum devices. For the generation of spin-superfluid systems, a detailed understanding of the build-up of coherence and relaxation is necessary. However, to determine the relevant parameters for robust coherence properties and faithfully witnessing thermalization, the direct access to space- and time-resolved spin observables is needed. Here, we study the thermalization of an easy-plane ferromagnet employing a homogeneous one-dimensional spinor Bose gas. Building on the pristine control of preparation and readout we demonstrate the dynamic emergence of long-range coherence for the spin field and verify spin-superfluidity by experimentally testing Landau's criterion. We reveal the structure of the emergent quasi-particles: one 'massive'(Higgs) mode, and two 'massless' (Goldstone) modes - a consequence of explicit and spontaneous symmetry breaking, respectively. Our experiments allow for the first time to observe the thermalization of an easy-plane ferromagnetic Bose gas; we find agreement for the relevant momentum-resolved observables with a thermal prediction obtained from an underlying microscopic model within the Bogoliubov approximation. Our methods and results pave the way towards a quantitative understanding of condensation dynamics in large magnetic spin systems and the study of the role of entanglement and topological excitations for its thermalization.

Inducing spin-order with an impurity: phase diagram of the magnetic Bose polaron

We investigate the formation of magnetic Bose polaron, an impurity atom dressed by spin-wave excitations, in a one-dimensional spinor Bose gas. Within an effective potential model, the impurity is strongly confined by the host excitations which can even overcome the impurity-medium repulsion leading to a self-localized quasi-particle state. The phase diagram of the attractive and self-bound repulsive magnetic polaron, repulsive non-magnetic (Fröhlich-type) polaron and impurity-medium phase-separation regimes is explored with respect to the Rabi-coupling between the spin components, spin–spin interactions and impurity-medium coupling. The residue of such magnetic polarons decreases substantially in both strong attractive and repulsive branches with strong impurity-spin interactions, illustrating significant dressing of the impurity. The impurity can be used to probe and maneuver the spin polarization of the magnetic medium while suppressing ferromagnetic spin–spin correlations. It is shown that mean-field theory fails as the spinor gas approaches immiscibility since the generated spin-wave excitations are prominent. Our findings illustrate that impurities can be utilized to generate controllable spin–spin correlations and magnetic polaron states which can be realized with current cold atom setups.

False-vacuum decay in an ultracold spin-1 Bose gas

We propose an ultracold atom analogue of early universe vacuum decay using all three states of a spin-1 Bose gas. We consider a one-dimensional system with both radio frequency and optical Raman coupling between internal states. An advantage of our proposal is the lack of a time-modulated coupling, which can lead to instabilities. Within the elaborate phase structure of the system we identify an effective Klein-Gordon field and use Gross-Pitaevskii simulations within the truncated Wigner approximation to model the decay of its false vacuum. We examine the dependence of the rate of vacuum decay on particle density for $^{7}$Li and $^{41}$K and find reasonable agreement with instanton methods.

Dynamical Zeeman resonance in spin-orbit-coupled spin-1 Bose gases

We predict a dynamical resonant effect, which is driven by externally applied linear and quadratic Zeeman fields, in a spin-orbit-coupled spin-1 Bose-Einstein condensate. The Bose-Einstein condensate is assumed to be initialized in some superposed state of Zeeman sublevels and subject to a sudden shift of the trapping potential. It is shown that the time-averaged center-of-mass oscillation and the spin polarizations of the Bose-Einstein condensate exhibit remarkable resonant peaks when the Zeeman fields are tuned to certain strengths. The underlying physics behind this resonance can be traced back to the out-of-phase interference of the dynamical phases carried by different spinorbit states. By analyzing the single particle spectrum, the resonant condition is summarized as a simple algebraic relation, connecting the strengths of the linear and quadratic Zeeman fields. This property is potentially applicable in quantum information and quantum precision measurement.

Dark-antidark spinor solitons in spin-1 Bose gases

We consider a one-dimensional trapped spin-1 Bose gas and numerically explore families of its solitonic solutions, namely antidark-dark-antidark (ADDAD), as well as dark-antidark-dark (DADD) solitary waves. Their existence and stability properties are systematically investigated within the experimentally accessible easy-plane ferromagnetic phase by means of a continuation over the atom number as well as the quadratic Zeeman energy. It is found that ADDADs are substantially more dynamically robust than DADDs. The latter are typically unstable within the examined parameter range. The dynamical evolution of both of these states is explored and the implication of their potential unstable evolution is studied. Some of the relevant observed possibilities involve, e.g., symmetry-breaking instability manifestations for the ADDAD, as well as splitting of the DADD into a right- and a left-moving dark-antidark pair with the anti-darks residing in a different component as compared to prior to the splitting. In the latter case, the structures are seen to disperse upon long-time propagation.

Low-Density Spinor Bose Gas of Particles with Arbitrary Spin

Low-Density Spinor Bose Gas of Particles with Arbitrary Spin

Spontaneous formation of vortices and gray solitons in a spinor polariton fluid under coherent driving

A new mechanism of parity breakdown in a spinor Bose gas is predicted; it causes a single-mode state of polaritons to be spontaneously divided into different polarization domains which annihilate each other at the interface areas. In a polariton wire, such interface is a dark soliton that can run in space without dissipation. In a planar cavity, quantized vortices arise in which phase difference of orthogonally polarized components makes one complete turn around the core. Coupled vortex-antivortex pairs and straight filaments can form in analogy to Bose-Einstein condensates and superconductors. However, the rotational symmetry is broken even for individual vortices, which makes them interact on a large scale and form internally ordered structures. These states come into being under resonant excitation if the spin coupling rate significantly exceeds the decay rate.

Many-body effects on second-order phase transitions in spinor Bose-Einstein condensates and breathing dynamics

We unravel the correlation effects of the second-order quantum phase transitions emerging on the ground state of a harmonically trapped spin-1 Bose gas, upon varying the involved Zeeman terms, as well as its breathing dynamics triggered by quenching the trapping frequency. It is found that the boundaries of the associated magnetic phases are altered in the presence of interparticle correlations for both ferromagnetic and anti-ferromagnetic spin-spin interactions, an effect which becomes more prominent in the few-body scenario. Most importantly, we unveil a correlation-induced shrinking of the anti-ferromagnetic and broken-axisymmetry phases implying that ground states with bosons polarized in a single spin-component are favored. Turning to the dynamical response of the spinor gas it is shown that its breathing frequency is independent of the system parameters while correlations lead to the formation of filamentary patterns in the one-body density of the participating components. The number of filaments is larger for increasing spin-independent interaction strengths or for smaller particle numbers. Each filament maintains its coherence and exhibits an anti-correlated behavior while distinct filaments show significant losses of coherence and are two-body correlated. Interestingly, we demonstrate that for an initial broken-axisymmetry phase an enhanced spin-flip dynamics takes place which can be tuned either via the linear Zeeman term or the quench amplitude.

Nonlinear modes in spatially confined spin–orbit-coupled Bose–Einstein condensates with repulsive nonlinearity

It was found that spatially confined spin-orbit (SO) coupling, which can be induced by illuminating Bose-Einstein condensates (BECs) with a Gaussian laser beam, can help trap a spinor Bose gas in multi-dimensional space. Previous works on this topic were all based on a Boson gas featuring an attractive interaction. In this paper, we consider the trapping effect in the case in which the Boson gas features a repulsive interaction. After replacing the repulsive effect, stable excited modes of semi-vortex (SV) type and mixed-mode (MM) type, which cannot be created in a boson gas with attractive interactions, can be found in the current setting. The trapping ability and the capacity of the confined SO coupling versus the degree of the repulsive strength as well as the order of the excited mode are systematically discussed firstly through the paper. Moreover, the stability of the nonlinear mode trapped in this system with a moving reference frame is also discussed. Unlike the system with homogeneous SO coupling, two different types of stationary mobility modes can be stabilized when the SO coupling moves in the x- and y- directions, respectively. This finding indicates that the system with moving confined SO coupling features a typical anisotropic character that differs from the system with moving homogeneous SO coupling.

Experimental extraction of the quantum effective action for a non-equilibrium many-body system

Far-from-equilibrium situations are ubiquitous in nature. They are responsible for a wealth of phenomena, which are not simple extensions of near-equilibrium properties, ranging from fluid flows turning turbulent to the highly organized forms of life. On the fundamental level, quantum fluctuations or entanglement lead to novel forms of complex dynamical behaviour in many-body systems for which a description as emergent phenomena can be found within the framework of quantum field theory. A central quantity in these efforts, containing all information about the measurable physical properties, is the quantum effective action. Though the problem of non-equilibrium quantum dynamics can be exactly formulated in terms of the quantum effective action, the solution is in general beyond capabilities of classical computers. In this work, we present a strategy to determine the non-equilibrium quantum effective action using analog quantum simulators, and demonstrate our method experimentally with a quasi one-dimensional spinor Bose gas out of equilibrium. Building on spatially resolved snapshots of the spin degree of freedom, we infer the quantum effective action up to fourth order in an expansion in one-particle irreducible correlation functions at equal times. We uncover a strong suppression of the irreducible four-vertex emerging at low momenta, which solves the problem of dynamics in the highly occupied regime far from equilibrium where perturbative descriptions fail. Similar behaviour in this non-pertubative regime has been proposed in the context of early-universe cosmology. Our work constitutes a new realm of large-scale analog quantum computing, where the high level of control of synthetic quantum systems provides the means for the solution of long-standing theoretical problems in high-energy and condensed matter physics with an experimental approach.

Correlation functions of one-dimensional strongly interacting two-component gases

We address the problem of calculating the correlation functions of one-dimensional two-component gases with strong repulsive contact interactions. The model considered in this paper describes particles with fractional statistics and in appropriate limits reduces to the Gaudin-Yang model or the spinor Bose gas. In the case of impenetrable particles we derive a Fredholm determinant representation for the temperature-, time-, and space-dependent correlation functions which is very easy to implement numerically and constitute the starting point for the analytical investigation of the asymptotics. Making use of this determinant representation and the solution of an associated Riemann-Hilbert problem we derive the low-energy asymptotics of the correlators in the spin-incoherent regime characterized by near ground-state charge degrees of freedom but a highly thermally disordered spin sector. The asymptotics present features reminiscent of spin-charge separation with the spin part exponentially decaying in space separation and oscillating with a period proportional to the statistics parameter while the charge part presents scaling with anomalous exponents which cannot be described by any unitary conformal field theory. The momentum distribution and the Fourier transform of the dynamical Green's function are asymmetrical for arbitrary statistics, a direct consequence of the broken space-reversal symmetry. Due to the exponential decay the momentum distribution $n(k)$ at zero temperature does not present algebraic singularities but the tails obey the universal decay $\lim_{k\rightarrow\pm\infty}n(k)\sim C/k^4$ with the amplitude $C$ given by Tan's contact. As a function of the statistics parameter the contact is a monotonic function reaching its minimum for the fermionic system and the maximum for the bosonic system.

Nonequilibrium quantum phase transition in a spinor quantum gas in a lattice coupled to a membrane

Recently, a novel kind of hybrid atom-optomechanical system, consisting of atoms in a lattice coupled to a membrane, has been experimentally realized [Vochezer {\it et al.,} Phys. Rev. Lett. \textbf{120}, 073602 (2018)], which promises a viable contender in the competitive field of simulating non-equilibrium many-body physics. Here we are motivated to investigate a spinor Bose gas coupled to a vibrational mode of a nano-membrane, focusing on analyzing the role of the spinor degrees of freedom therein. Through an adiabatic elimination of the degrees of freedom of the quantum oscillator, we derive an effective Hamiltonian which reveals a competition between the force localizing the atoms and the membrane displacement. We analyze the dynamical stability of the steady state using Bogoliubov-de Gennes approach and derive the stationary phase diagram in the parameter space. We investigate the non-equilibrium quantum phase transition from a localized symmetric state of the atom cloud to a shifted symmetry-broken state, where we present a detailed analysis of the effects of the spin degree of freedom. Our work presents a simple way to study the effects of the spinor degree of freedom on the non-equilibrium nonlinear phenomena that is complementary to ongoing experiments on the hybrid atom-optomechanical system.

Stability analysis of ground states in a one-dimensional trapped spin-1 Bose gas

In this work we study the stability properties of the ground states of a spin-1 Bose gas in presence of a trapping potential in one spatial dimension. To set the stage we first map out the phase diagram for the trapped system by making use of a, so-called, continuous-time Nesterov method. We present an extension of the method, which has been previously applied to one-component systems, to our multi-component system. We show that it is a powerful and robust tool for finding the ground states of a physical system without the need of an accurate initial guess. We subsequently solve numerically the Bogoliubov de-Gennes equations in order to analyze the stability of the ground states of the trapped spin-1 system. We find that the trapping potential retains the overall structure of the stability diagram, while affecting the spectral details of each of the possible ground state waveforms. It is also found that the peak density of the trapped system is the characteristic quantity describing dynamical instabilities in the system. Therefore replacing the homogeneous density with the peak density of the trapped system leads to good agreement of the homogeneous Bogoliubov predictions with the numerically observed maximal growth rates of dynamically unstable modes. The stability conclusions in the one-dimensional trapped system are independent of the spin coupling strength and the normalized trap strength over several orders of magnitude of their variation.

Berezinskii–Kosterlitz–Thouless Transition of Spin-1 Spinor Bose Gases in the Presence of the Quadratic Zeeman Effect

We numerically study the Berezinskii-Kosterlitz-Thouless (BKT) transition of a spin-1 spinor Bose gas under the quadratic Zeeman effect. A calculation of the mass and spin superfluid densities shows that (i) the BKT transition occurs only when vortices are classified by the integer group $\mathbb{Z}$, and $\mathbb{Z}_2$ vortices do not contribute to the BKT transition, (ii) the two BKT transition temperatures for mass and spin superfluid densities are different for a positive quadratic Zeeman effect and equal for a negative quadratic Zeeman effect, and (iii) the universal relation of the superfluid densities at the BKT transition temperature is changed when multiple kinds of vortices contribute to the transition. We have further found that (iv) spin-singlet pairs in non-magnetic states show the quasi-off-diagonal-long-range order at the different temperature lower than the BKT transition temperature, giving the new universal relation of the superfluid density.

Violation of single-length-scaling dynamics via spin vortices in an isolated spin-1 Bose gas

We consider the phase ordering dynamics of an isolated quasi-two-dimensional spin-1 Bose gas quenched into an easy-plane ferromagnetic phase. Preparing the initial system in an unmagnetized anti-ferromagnetic state the subsequent ordering involves both polar core and Mermin-Ho spin vortices, with the ratio between the different vortices controllable by the quench parameter. Ferromagnetic domain growth occurs as these vortices annihilate. The distinct dynamics of the two types of vortices means that the domain growth law is determined by two macroscopic length scales, violating the standard dynamic scaling hypothesis. Nevertheless we find that universality of the ordering process manifests in the decay laws for the spin vortices.

Flemish Strings of Magnetic Solitons and a Nonthermal Fixed Point in a One-Dimensional Antiferromagnetic Spin-1 Bose Gas.

Thermalization in a quenched one-dimensional antiferromagnetic spin-1 Bose gas is shown to proceed via a nonthermal fixed point through annihilation of Flemish-string bound states of magnetic solitons. A possible experimental situation is discussed.