Cold Quantum Gases Research Articles

Two-particle bound states on a lattice

Two-particle lattice states are important for physics of magnetism, superconducting oxides, and cold quantum gases. The quantum-mechanical lattice problem is exactly solvable for finite-range interaction potentials. A two-body Schrödinder equation can be reduced to a system of linear equations whose numbers scale with the number of interacting sites. For the simplest cases such as on-site or nearest-neighbor attractions, many pair properties can be derived analytically, although final expressions can be quite complicated. In this work, we systematically investigate bound pairs in one-, two-, and three-dimensional lattices. We derive pairing conditions, plot phase diagrams, and compute energies, effective masses and radii. Along the way, we analyze nontrivial physical effects such as light pairs and the dependence of binding thresholds on pair momenta. At the end, we discuss the preformed-pair mechanism of superconductivity and stability of many-pair systems against phase separation. The paper is a combination of original work and pedagogical tutorial.

Gaussian variational method to Fermi-Hubbard model in one and two dimensions

The study of ground-state properties of the Fermi-Hubbard model is a long-lasting task in the research of strongly correlated systems, and is crucial for the understanding of notable quantum phenomena including superconductivity and magnetism. Owing to the exponentially growing complexity of the system, a quantitative analysis usually demands high computational cost and is restricted to small samples, especially in two or higher dimensions. Here, we introduce a variational method in the frame of fermionic Gaussian states, and obtain the ground states of one- and two-dimensional attractive Hubbard models via imaginary-time evolution. We calculate the total energy and benchmark the results in a wide range of interaction strength and filling factor with those obtained via exact two-body results, the density matrix renormalization group based on matrix product states (MPS), and projector Quantum Monte Carlo (QMC) method. For both 1D and 2D cases, the Gaussian variational method presents accurate results for total energy with a maximum systematic error in the intermediate interaction region. The accuracy of these results has negligible dependence on the system size. We further calculate the double occupancy and find excellent agreement with MPS and QMC, as well as the experimental results of cold quantum gases in optical lattices. The results suggest that the Gaussian pairing state is a good approximation to the ground states of attractive Hubbard model, in particular in the strong and weak coupling limits. Moreover, we generalize the method to the attractive Hubbard model with a finite spin-polarization, which can be mapped to the repulsive interaction case via particle-hole transformation, and obtain accurate results of ground state energy and double occupancy. Our work demonstrates the ability of the Gaussian variational method to extract ground state properties of strongly correlated many-body systems with negligible computational cost, especially of large size and in higher dimensions.

Soliton molecules in coupled dipolar Bose–Einstein condensates with spin-orbit coupling

Recent research works on ultra cold quantum gases demonstrated that dipolar Bose–Einstein condensates (BECs) exhibit rich spatiotemporal dynamic where both local and nonlocal interactions are considered. We explore theoretically the possibility of controlling the formation and dynamics of soliton molecules in binary dipolar condensates with spin-orbit coupling (SOC). We exploit the variational technique to derive the new equations of motion for the widths and amplitudes, the effective potential and the oscillation frequency of the molecules. Our study confirms the existence of stable localized bound states in an optical potential. We find that the integrity of the molecules is influenced by the physical parameters, notably the local and nonlocal interactions with the SOC. These parameters are carefully chosen by the Vakhitov–Kolokolov (VK) criterion to ensure the stability of the molecules. We present the results of numerical experiments and confirm the analytical predictions. Moreover, we show the soliton–soliton interaction in each molecule when the local interactions are strong.

Precision measurement of atom-dimer interaction in a uniform planar Bose gas

Cold quantum gases, when acted upon by electromagnetic fields, can give rise to samples where isolated atoms coexist with dimers or trimers, which raises the question of the interactions between these various constituents. Here we perform microwave photoassociation in a degenerate gas of Rb87 atoms to create weakly bound dimers in their electronic ground level. We determine the complete energy diagram of one hyperfine manifold of the least-bound level, which we accurately reproduce with a simple model. Then, from the density-induced shift of the photoassociation line, we measure the atom-dimer scattering length for two weakly bound states of the molecular potential.Received 14 November 2022Accepted 12 January 2023DOI:https://doi.org/10.1103/PhysRevResearch.5.L012020Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBose-Einstein condensatesCold and ultracold moleculesCold atoms & matter wavesInteratomic & molecular potentialsPhotoassociationUltracold collisionsVan der Waals interactionAtomic, Molecular & Optical

Compressibility and the equation of state of an optical quantum gas in a box.

The compressibility of a medium, quantifying its response to mechanical perturbations, is a fundamental property determined by the equation of state. For gases of material particles, studies of the mechanical response are well established, in fields from classical thermodynamics to cold atomic quantum gases. We demonstrate a measurement of the compressibility of a two-dimensional quantum gas of light in a box potential and obtain the equation of state for the optical medium. The experiment was carried out in a nanostructured dye-filled optical microcavity. We observed signatures of Bose-Einstein condensation at high phase-space densities in the finite-size system. Upon entering the quantum degenerate regime, the measured density response to an external force sharply increases, hinting at the peculiar prediction of an infinite compressibility of the deeply degenerate Bose gas.

Time-dependent entropy of a cooling Bose gas

Exact analytic solutions of a nonlinear boson diffusion equation with suitable initial conditions that account for evaporative cooling of ultracold atoms, plus boundary conditions at the singularity are presented, and used to calculate the time-dependent entropy of a cold quantum gas.

Postquench gap dynamics of two-band superconductors

Recent experimental progress in the fields of cold quantum gases and ultrafast optical spectroscopy of quantum materials allows to controllably induce and probe non-adiabatic dynamics of superconductors and superfluids. The time-evolution of the gap function before relaxation with the lattice is determined by the superposition of coherently evolving individual Cooper pairs within the manifold of the Bardeen-Cooper-Schrieffer (BCS) wavefunction. While dynamics following an abrupt quench of the pairing interaction strength in the single-band BCS model has been exactly solved due to the integrability of the model, the dynamics of post-quench multi-band superconductors remain under scrutiny. Here, we develop a generalization of the Volkov-Kogan Laplace-space perturbative method that allows us to determine the non-adiabatic gap dynamics of two-band fully gapped superconductors for a wide range of quench amplitudes. Our approach expands the long-time dynamics around the steady-state asymptotic value of the gap, which is self-consistently determined, rather than around the equilibrium value of the gap. We explicitly demonstrate that this method recovers the exact solution of the long-time gap dynamics in the single-band case and perfectly agrees with a numerical solution of the two-band model. We discover that dephasing of Cooper pairs from different bands leads to faster collisionless relaxation of the gap oscillation with a power-law of $t^{-3/2}$ instead of the well-known $t^{-1/2}$ behavior found in the single-band case. Furthermore, the gap oscillations display beating patterns arising from the existence of two different asymptotic gap values. Our results have important implications to a variety of two-band superconductors driven out of equilibrium, such as iron-based superconductors, MgB$_{2}$, and SrTiO$_{3}$.

Atomtronics with a spin: Statistics of spin transport and nonequilibrium orthogonality catastrophe in cold quantum gases

We propose to investigate the full counting statistics of nonequilibrium spin transport with an ultracold atomic quantum gas. The setup makes use of the spin control available in atomic systems to generate spin transport induced by an impurity atom immersed in a spin-imbalanced two-component Fermi gas. In contrast to solid-state realizations, in ultracold atoms spin relaxation and the decoherence from external sources is largely suppressed. As a consequence, once the spin current is turned off by manipulating the internal spin degrees of freedom of the Fermi system, the nonequilibrium spin population remains constant. Thus one can directly count the number of spins in each reservoir to investigate the full counting statistics of spin flips, which is notoriously challenging in solid state devices. Moreover, using Ramsey interferometry, the dynamical impurity response can be measured. Since the impurity interacts with a many-body environment that is out of equilibrium, our setup provides a way to realize the non-equilibrium orthogonality catastrophe. Here, even for spin reservoirs initially prepared in a zero-temperature state, the Ramsey response exhibits an exponential decay, which is in contrast to the conventional power-law decay of Anderson's orthogonality catastrophe. By mapping our system to a multi-step Fermi sea, we are able to derive analytical expressions for the impurity response at late times. This allows us to reveal an intimate connection of the decay rate of the Ramsey contrast and the full counting statistics of spin flips.

Local equilibration of fermions and bosons

Local kinetic equilibration is a prerequisite for hydrodynamics to be valid. Here it is described through a nonlinear diffusion equation for finite systems of fermions and bosons. The model is solved exactly for constant transport coefficients in both cases. It has the proper Fermi-Dirac and Bose-Einstein equilibrium limits and can replace the relaxation-time approximation (RTA). The microscopic transport coefficients are determined through the macroscopic variables temperature and local equilibration time. Applications to the transverse energy of quarks and gluons in the initial stages of central relativistic heavy-ion collisions, and to bosonic and fermionic atoms at low energies appropriate for cold quantum gases are discussed.

Electromagnetically induced transparency in a spin-orbit-coupled finite-temperature cold atomic ensemble

We investigated the electromagnetically induced transparency in spin-orbit-coupled finite-temperature cold quantum gases. We showed that spin-orbit coupling can induce an additional frequency shift in the absorption line, which can be observed nondestructively from the electromagnetically induced transparency spectroscopy. As an alternative method this shift can be used to detect and measure the spin-orbit coupling strength. The spin-orbit coupling can also be used as a switch to control laser light propagation in this medium.

An exactly solvable model for equilibration in bosonic systems

An analytical model for the kinetic equilibration of finite Bose systems is outlined. The corresponding transport equation is solved exactly through a nonlinear transformation. The model is applied to the equilibration of a cold quantum gas including implicitly the formation of a Bose-Einstein condensate through particle-number conservation.

Equilibration in finite Bose systems

The equilibration of a finite Bose system is modeled using a gradient expansion of the collision integral that leads to a nonlinear transport equation. For constant transport coefficients, it is solved in closed form through a nonlinear transformation. Using schematic initial conditions, the exact solution and the equilibration time are derived and compared to the corresponding case for fermions. Applications to the fast equilibration of the gluon system created initially in relativistic heavy-ion collisions, and to cold quantum gases are envisaged.

Noise spectroscopy with a quantum gas

We report on the spectral analysis and the local measurement of intensity correlations of microwave fields using ultra cold quantum gases. The fluctuations of the electromagnetic field induce spin flips in a magnetically trapped quantum gas and generate a multi-mode atomlaser. The output of the atomlaser is measured with high temporal resolution on the single atom level, from which the spectrum and intensity correlations of the generating microwave field are reconstructed. We give a theoretical description of the atomlaser output and its correlations in response to resonant microwave fields and verify the model with measurements on an atom chip. The measurement technique is applicable for the local analysis of classical and quantum noise of electromagnetic fields, for example on chips, in the vicinity of quantum electronic circuits.

A high resolution ion microscope for cold atoms

We report on an ion-optical system that serves as a microscope for ultracold ground state and Rydberg atoms. The system is designed to achieve a magnification of up to 1000 and a spatial resolution in the 100 nm range, thereby surpassing many standard imaging techniques for cold atoms. The microscope consists of four electrostatic lenses and a microchannel plate in conjunction with a delay line detector in order to achieve single particle sensitivity with high temporal and spatial resolution. We describe the design process of the microscope including ion-optical simulations of the imaging system and characterize aberrations and the resolution limit. Furthermore, we present the experimental realization of the microscope in a cold atom setup and investigate its performance by patterned ionization with a structure size down to 2.7 μm. The microscope meets the requirements for studying various many-body effects, ranging from correlations in cold quantum gases up to Rydberg molecule formation.

High-power, micro-integrated diode laser modules at 767 and 780 nm for portable quantum gas experiments.

We present micro-integrated diode laser modules operating at wavelengths of 767 and 780 nm for cold quantum gas experiments on potassium and rubidium. The master-oscillator-power-amplifier concept provides both narrow linewidth emission and high optical output power. With a linewidth (10 μs) below 1 MHz and an output power of up to 3 W, these modules are specifically suited for quantum optics experiments and feature the robustness required for operation at a drop tower or on-board a sounding rocket. This technology development hence paves the way toward precision quantum optics experiments in space.

Quantum spin dimers from chiral dissipation in cold-atom chains.

We consider the nonequilibrium dynamics of a driven dissipative spin chain with chiral coupling to a one-dimensional (1D) bosonic bath, and its atomic implementation with a two-species mixture of cold quantum gases. The reservoir is represented by a spin-orbit coupled 1D quasicondensate of atoms in a magnetized phase, while the spins are identified with motional states of a separate species of atoms in an optical lattice. The chirality of reservoir excitations allows the spins to couple differently to left- and right-moving modes, which in our atomic setup can be tuned from bidirectional to purely unidirectional. Remarkably, this leads to a pure steady state in which pairs of neighboring spins form dimers that decouple from the remainder of the chain. Our results also apply to current experiments with two-level emitters coupled to photonic waveguides.

Induced delocalization by correlation and interaction in the one-dimensional Anderson model

We consider long-range correlated disorder and mutual interacting particles according to a dipole-dipole coupling as modifications to the one-dimensional Anderson model. Technically we rely on the (numerical) exact diagonalization of the system's Hamilitonian. From the perspective of different localization measures we confirm and extend the picture of the emergence of delocalized states with increasing correlations. Beside these studies a definition for multi-particle localization is proposed. In the case of two interacting bosons we observe a sensitivity of localization with respect to the range of the particle-particle interaction and insensitivity to the coupling's sign, which should stimulate new theoretical approaches and experimental investigations with e.g. dipolar cold quantum gases. This revised manuscript is much more explicit compared to the initial version of the paper. Major extensions have been applied to Sects. II and III where we updated and added figures and we more extensively compared our results to the literature. Furthermore, Sect. III additionally contains a phenomenological line of reasoning that bridges from delocalization by correlation to delocalization by interaction on the basis of the multi-particle Hamilton matrix.

Colloquium: Artificial gauge potentials for neutral atoms

When a neutral atom moves in a properly designed laser field, its center-of-mass motion may mimic the dynamics of a charged particle in a magnetic field, with the emergence of a Lorentz-like force. In this Colloquium we present the physical principles at the basis of this artificial (synthetic) magnetism and relate the corresponding Aharonov-Bohm phase to the Berry's phase that emerges when the atom follows adiabatically one of its dressed states. We also discuss some manifestations of artificial magnetism for a cold quantum gas, in particular in terms of vortex nucleation. We then generalise our analysis to the simulation of non-Abelian gauge potentials and present some striking consequences, such as the emergence of an effective spin-orbit coupling. We address both the case of bulk gases and discrete systems, where atoms are trapped in an optical lattice.

Dynamics of a cold quantum gas in a δ-split one-dimensional potential well

Dynamics of a wave function in a non-symmetrically split (spatially asymmetric) doublewell potential is considered. We study the dependence of the probability of well-to-well transitions on the degree of spatial asymmetry of well sizes and show that the quantum tunneling between the wells is significantly suppressed by this asymmetry. Practically complete suppression occurs at five-ten percent asymmetry. This is close to the threshold of sensitivity of contemporary experimental schemes for creating two-well potentials. We predict the phenomenon of resonance in quantum tunneling of considered states. We have also shown that an incoherently prepared superposition state tunnels in a double-well potential almost in the same way as a perfectly coherent state.

Finite-temperature coherence of the ideal Bose gas in an optical lattice

In current experiments with cold quantum gases in periodic potentials, interference fringe contrast is typically the easiest signal in which to look for effects of nontrivial many-body dynamics. In order better to calibrate such measurements, we analyze the background effect of thermal decoherence as it occurs in the absence of dynamical interparticle interactions. We study the effect of optical lattice potentials, as experimentally applied, on the condensed fraction of a noninteracting Bose gas in local thermal equilibrium at finite temperatures. We show that the experimentally observed decrease of the condensate fraction in the presence of the lattice can be attributed, up to a threshold lattice height, purely to ideal-gas thermodynamics; conversely, we confirm that sharper decreases in first-order coherence observed in stronger lattices are indeed attributable to many-body physics. Our results also suggest that the fringe visibility ``kinks'' observed in Gerbier et al., Phys. Rev. Lett. 95, 050404 (2005) may be explained in terms of the competition between increasing lattice strength and increasing mean gas density, as the Gaussian profile of the red-detuned lattice lasers also increases the effective strength of the harmonic trap.