Ultracold Atomic Systems Research Articles

Observation of two-dimensional Anderson localisation of ultracold atoms

Anderson localisation —the inhibition of wave propagation in disordered media— is a surprising interference phenomenon which is particularly intriguing in two-dimensional (2D) systems. While an ideal, non-interacting 2D system of infinite size is always localised, the localisation length-scale may be too large to be unambiguously observed in an experiment. In this sense, 2D is a marginal dimension between one-dimension, where all states are strongly localised, and three-dimensions, where a well-defined phase transition between localisation and delocalisation exists as the energy is increased. Here, we report the results of an experiment measuring the 2D transport of ultracold atoms between two reservoirs, which are connected by a channel containing pointlike disorder. The design overcomes many of the technical challenges that have hampered observation of localisation in previous works. We experimentally observe exponential localisation in a 2D ultracold atom system.

Fermion parity gap and exponential ground state degeneracy of the one-dimensional Fermi gas with intrinsic attractive interaction

We examine the properties of a one-dimensional (1D) Fermi gas with attractive intrinsic (Hubbard) interactions in the presence of spin-orbit coupling and Zeeman field by numerically computing the pair binding energy, excitation gap, and susceptibility to local perturbations using the density matrix renormalization group. Such a system can, in principle, be realized in a system of ultracold atoms confined in a 1D optical lattice. We note that, in the presence of spatial interfaces introduced by a smooth parabolic potential, the pair binding and excitation energy of the system decays exponentially with the system size, pointing to the existence of an exponential ground state degeneracy, and is consistent with recent works. However, the susceptibility of the ground state degeneracy of this number-conserving system to local impurities indicates that the energy gap vanishes as a power law with the system size in the presence of local perturbations. We compare this system with the more familiar system of an Ising antiferromagnet in the presence of a transverse field realized with Rydberg atoms and argue that the exponential splitting in the clean number-conserving 1D Fermi system is similar to a phase with only conventional order.

Phase diagram and optimal control for n-tupling discrete time crystal

A remarkable consequence of spontaneously breaking the time translational symmetry in a system, is the emergence of time crystals. In periodically driven systems, discrete time crystals (DTC) can be realized which have a periodicity that is n times the driving period. However, all of the experimental observations have been performed for period-doubling and period-tripling DTC. Novel physics can arise by simulating many-body physics in the time domain, which would require a genuine realisation of the n-tupling DTC. A system of ultra-cold bosonic atoms bouncing resonantly on an oscillating mirror is one of the models that can realise large period DTC. The preparation of DTC demands control in creating the initial distribution of the ultra-cold bosonic atoms along with the mirror frequency. In this work, we demonstrate that such DTC is robust against perturbations to the initial distribution of atoms. We show how Bayesian methods can be used to enhance control in the preparation of the initial state as well as to efficiently calculate the phase diagram for such a model. Moreover, we examine the stability of DTCs by analyzing quantum many-body fluctuations and show that they do not reveal signatures of heating.

Optimal control for generating excited state expansion in ring potential

AbstractWe applied an optimal control algorithm to an ultra-cold atomic system for constructing an atomic Sagnac interferometer in a ring trap. We constructed a ring potential on an atom chip by using an RF-dressed potential. A field gradient along the radial direction in a ring trap known as the dimple-ring trap is generated by using an additional RF field. The position of the dimple is moved by changing the phase of the RF field [1]. For Sagnac interferometers, we suggest transferring Bose–Einstein condensates to a dimple-ring trap and shaking the dimple potential to excite atoms to the vibrational-excited state of the dimple-ring potential. The optimal control theory is used to find a way to shake the dimple-ring trap for an excitation. After excitation, atoms are released from the dimple-ring trap to a ring trap by adiabatically turning off the additional RF field, and this constructs a Sagnac interferometer when opposite momentum components are overlapped. We also describe the simulation to construct the interferometer.

Experimental realization of spin-tensor momentum coupling in ultracold Fermi gases

We experimentally realize the spin-tensor momentum coupling (STMC) using the three ground Zeeman states coupled by three Raman laser beams in ultracold atomic system of $^{40}$K Fermi atoms. This new type of STMC consists of two bright-state bands as a regular spin-orbit coupled spin-1/2 system and one dark-state middle band. Using radio-frequency spin-injection spectroscopy, we investigate the energy band of STMC. It is demonstrated that the middle state is a dark state in the STMC system. The realized energy band of STMC may open the door for further exploring exotic quantum matters.

Optimality and universality in quantum Zeno dynamics

The effective lifetime of a quantum state can increase (the quantum Zeno effect) or decrease (the quantum anti-Zeno effect) in the response to increasing frequency of the repeated measurements and the multiple transitions between these two regimes are potentially possible within the same system. An interesting question arising in this regards is how to choose the optimal schedule of repeated measurements to achieve the maximal possible decay rate of a given quantum state. Addressing the issue of optimality in the quantum Zeno dynamics, we derive a range of rigorous results, which are, due to generality of the theoretical framework adopted here, applicable to the majority of models appeared in the quantum Zeno literature. In particular, we prove the universal dominance of the regular stroboscopic sampling in the sense that it always provides the shortest expected decay time among all possible measurement procedures. However, the implementation of the stroboscopic protocol requires the knowledge of the optimal sampling period which may depend on the fine details of the quantum problem. We demonstrate that this difficulty can be overcome with the tricky non-regular measurement schedule inspired by the scale-free restart strategy used to speed up the completion of the probabilistic algorithms and Internet tasks in computer science as it allows to achieve a near-optimal decay rate in the absence of detailed knowledge of the underlying quantum statistics. Besides, our general approach reveals unexpected universality displayed by the quantum systems subject to the optimally tuned rate of Poissonian measurements and the simple statistical criteria to discriminate between Zeno and anti-Zeno regimes following from this universality. We illustrate our findings with an example of Zeno dynamics in the system of optically-trapped ultra-cold atoms and discuss the implications arising from them.

Coupled first-order transitions and unconventional superfluidity in a Fermi-Bose mixture

A model of a mixture of spinless fermions and spin-zero hardcore bosons, with filling fractions $\rho_F$ and $\rho_B$, respectively, on a two-dimensional square lattice with {\em composite} hopping $t$ is presented. In this model, hopping swaps the locations of a fermion and a boson at nearest-neighbor sites. When $\rho_F+\rho_B=1$, the fermion hopping amplitude $\phi$ and boson superfluid amplitude $\psi$ are calculated in the ground state within a mean-field approximation. The Fermi sector is insulating ($\phi=0$) and the Bose sector is normal ($\psi=0$) for $0 \le \rho_F < \rho_c$. The model has {\em coupled first-order} transitions at $\rho_F = \rho_c \simeq 0.3$ where both $\phi$ and $\psi$ are discontinuous. The Fermi sector is metallic ($\phi>0$) and the Bose sector is superfluid ($\psi>0$) for $\rho_c < \rho_F < 1$. At $\rho_F=1/2$, fermion density of states $\rho$ has a van Hove singularity, the bulk modulus $\kappa$ displays a cusp-like singularity, the system has a density wave (DW) order, and $\phi$ and $\psi$ are maximum. At $\rho_F=\rho_{\kappa} \simeq 0.81$, $\kappa$ vanishes, becoming {\em negative} for $\rho_{\kappa}<\rho_F<1$. The role of composite hopping in the evolution of Fermi band dispersions and Fermi surfaces as a function of $\rho_F$ is highlighted. The estimate for BEC critical temperature is in the subkelvin range for ultracold atom systems and several hundred kelvins for possible solid-state examples of the model.

High-resolution imaging of Rydberg atoms in optical lattices using an aspheric-lens objective in vacuum.

We present a high-resolution, simple, and versatile system for imaging ultracold Rydberg atoms in optical lattices. The imaging objective is a single aspheric lens [with a working distance of 20.6 mm and a numerical aperture (NA) of 0.51] placed inside the vacuum chamber. Adopting a large-working-distance lens leaves room for electrodes and electrostatic shields to control electric fields around Rydberg atoms. With this setup, we achieve a Rayleigh resolution of 1.10 μm or 1.41λ (λ = 780 nm), limited by the NA of the aspheric lens. For systems of highly excited Rydberg states with blockade radii greater than a few μm, the resolution achieved is sufficient for studying many physical processes of interest.

Analog quantum simulation of the spinor-four Dirac equation with an artificial gauge field

A two-dimensional spatially and temporally modulated Wannier-Stark system of ultracold atoms in optical lattices is shown to mimic the behavior of a Dirac particle. Suitable additional modulations generate an artificial gauge field which simulates a magnetic field and imposes the use of the full spinor-four Dirac equation.

Probabilistic hysteresis in an isolated quantum system: The microscopic onset of irreversibility from a quantum perspective

Recently probabilistic hysteresis in isolated Hamiltonian systems of ultracold atoms has been studied in the limit of large particle numbers, where a semiclassical treatment is adequate. The origin of irreversibility in these sweep experiments, where a control parameter is slowly (adiabatically) tuned back and forth, turned out to be a passage blue back and forth across a separatrix (integrable case) or a passage in and out of a chaotic sea in phase space (chaotic case). Here we focus on the full quantum mechanical description of the integrable system and show how the semiclassical results emerge in the limit of large particle numbers. Instead of the crossing of a separatrix in phase space, where classical adiabaticity fails, the origin of irreversibility in the quantum system is a series of avoided crossings of the adiabatic energy levels: they become so close that already for modest particle numbers the change of the external parameter has to be unrealistically slow to reach the quantum adiabatic limit of perfectly reversible evolution. For a slow but finite sweep rate we find a broad regime where the quantum results agree with the semiclassical results, but only if besides the limit $N\to \infty$ an initial ensemble of states is considered, with sufficient initial energy width. For a single initial energy eigenstate we find in contrast that the backward sweep reveals strong quantum effects even for very large particle numbers.

Clustering of Four-Component Unitary Fermions.

Abinitio nuclear physics tackles the problem of strongly interacting four-component fermions. The same setting could foreseeably be probed experimentally in ultracold atomic systems, where two- and three-component experiments have led to major breakthroughs in recent years. Both due to the problem's inherent interest and as a pathway to nuclear physics, in this Letter we study four-component fermions at unitarity via the use of quantum MonteCarlo methods. We explore novel forms of the trial wave function and find one which leads to a ground state of the eight-particle system whose energy is almost equal to that of two four-particle systems. We investigate the clustering properties involved and also extrapolate to the zero-range limit. In addition to being experimentally testable, our results impact the prospects of developing nuclear physics as a perturbation around the unitary limit.

Universal momentum-to-real-space mapping of topological singularities

Topological properties of materials are typically presented in momentum space. Here, we demonstrate a universal mapping of topological singularities from momentum to real space. By exciting Dirac-like cones in photonic honeycomb (pseudospin-1/2) and Lieb (pseudospin-1) lattices with vortex beams of topological charge l, optimally aligned with a given pseudospin state s, we directly observe topological charge conversion that follows the rule l → l + 2s. Although the mapping is observed in photonic lattices where pseudospin-orbit interaction takes place, we generalize the theory to show it is the nontrivial Berry phase winding that accounts for the conversion which persists even in systems where angular momentum is not conserved, unveiling its topological origin. Our results have direct impact on other branches of physics and material sciences beyond the 2D photonic platform: equivalent mapping occurs for 3D topological singularities such as Dirac-Weyl synthetic monopoles, achievable in mechanical, acoustic, or ultracold atomic systems, and even with electron beams.

Thermalization and Nonequilibrium Steady States in a Few-Atom System

Abstract We investigate nonequilibrium steady states in an isolated system of few ultracold cesium atoms (Cs). Numerically and experimentally, we study the dynamics and fluctuations of the extracted position distributions and find the formation of nonthermal steady states for absent interactions. Atomic collisions in the s-wave regime, however, ensue thermalization of the few-particle system. We present numerical simulations of the microscopic equations of motion with a simple representation of the s-wave scattering events. Based on these simulations, a parameter range is identified, where the interaction between few atoms is sufficiently strong to thermalize the nonequilibrium steady state on experimentally accessible time scales, which can be traced by monitoring the atomic position distribution. Furthermore, the total energy distribution, which is also accessible experimentally, is found to be a powerful tool to observe the emergence of a thermal state. Our work provides a pathway for future experiments investigating the effect interactions in few-particle systems and underlines the role of fluctuations in investigating few-particle systems.

Some recent progresses on the study of ultracold quantum gases with spin-orbit coupling

Artificial synthetic gauge field and spin-orbit coupling has been extensively studied following their experimental realization in ultracold atomic systems. Thanks for the versatile controllability, such systems not only provide possibilities to simulate and study important models in multidisciplinary fields of physics, but also work as an excellent platform to engineer novel states of matter and quantum phenomena. This paper reviews some recent progresses on the study of ultracold atomic systems with spin-orbit coupling, focusing on the effects induced by dissipation, novel interaction forms, large symmetry of spins, and long-range interactions. The investigation in these aspects is closely related to the characteristics of ultracold atomic systems, hence can bring new inspirations and perspectives on the understanding of spin-orbit coupling. In this review, we firstly investigate the appearance of a topological superradiant state in a quasi-one-dimensional Fermi gas with cavity-assisted Raman process. A cavity-assisted spin-orbit coupling and a bulk gap opening at half filling will be induced by the superradiant light generated in the transversely driven cavity mode. The topological superradiant state and the corresponding topological phase transition in the system can be driven by this mechanism. Then, symmetry-protected topological states of interacting fermions will be introduced in a quasi-one-dimensional cold gas of alkaline-earth-like atoms. Raman-assisted spin-orbit couplings in the clock states, together with the spin-exchange interactions in the clock-state manifolds will give rise to symmetry-protected topological states for interacting fermions, by taking advantage of the separation of orbital and nuclear-spin degrees of freedom in these alkaline-earth-like atoms. Furthermore, we show that an exotic topological defect, double-quantum spin vortices, which are characterized by doubly quantized circulating spin currents and unmagnetized filled cores, can exist in the ground states of SU(3) spin-orbit-coupled Bose-Einstein condensates. It is found that the combined effects of SU(3) spin-orbit coupling and spin-exchange interaction determine the ground-state phase diagram. Finally, we demonstrate that spin-orbit coupling and soft-core long-range interaction can induce an exotic supersolid phase of Bose gas, with the emergence of spontaneous circulating particle current. This implies that a finite angular momentum can be generated with neither external rotation nor synthetic magnetic field, and the direction of the angular momentum can be altered by adjusting the strength of spin-orbit coupling or interatomic interaction.

An analysis of BCS-BEC crossover under three different approaches and evaluation of critical temperature Tlt;subgt;clt;/subgt;

BCS-BEC crossover regimes can be studied using three approaches (i) from 1D and 2D Hubbard model (ii) from two-channel model for system of ultra-cold alkali atoms (iii) via Feshbach resonance method. It has been observed that in 40K, the appearance of the condensate in BCS regime is accompanied by a significant decrease in the width of the non-condensate fraction. The origin of this phenomenon is yet unknown and requires further study. Another important aspect of the BCS-BEC transition is that one studies the nature of the condensate formed when the system is taken across the resonance. It is not known if the condensate is in the intermediate region of resonance then what will happen whether one will take the linear combination of Cooper pairs and tightly bound molecules or some complex state.

Time-optimal control of collisional SWAP gates in ultracold atomic systems

We use quantum optimal control to identify fast collision-based two-qubit $\sqrt{\text{SWAP}}$ gates in ultracold atoms. We show that a significant speed up can be achieved by optimizing the full gate instead of separately optimizing the merge-wait-separate sequence of the trapping potentials. Our optimal strategy does not rely on the atoms populating the lowest eigenstates of the merged potential, and it crucially includes accumulation of quantum phases before the potentials are fully merged. Our analyses transcend the particular trapping geometry, but to compare with previous works, we present systematic results for an optical lattice and find greatly improved gate durations and fidelities.

The ground state and the tunnelling dynamics of the Bose-Einstein condensate in a tilted shallow trap

The ground state and the tunnelling dynamics of the Bose-Einstein condensate (BEC) loaded in a tilted shallow trap is studied analytically and numerically. The stable bound state, the quasi-bound state and the diffusion state are predicted. The thresholds for transition between the different states are obtained and the stability diagram in parameter space is presented. The tunnelling dynamics of the system in different states is revealed. The shape of the potential well and the atomic interaction play important role and have coupled effect on the tunnelling dynamics of the system. Furthermore, the resonant tunnelling phenomenon in the parametrically modulated shallow trap is observed. The results show that when the modulating frequency approaches the dipolar mode of the system, resonant tunnelling occurs and the whole system is unstable. Our results provide a theoretical evidence for studying the tunnelling dynamics of the ultracold atomic system.

Floquet engineering of optical lattices with spatial features and periodicity below the diffraction limit

Floquet engineering or coherent time-periodic driving of quantum systems has been successfully used to synthesize Hamiltonians with novel properties. In ultracold atomic systems, this has led to experimental realizations of artificial gauge fields, topological bandstructures, and observation of dynamical localization, to name a few. Here we present a Floquet-based framework to stroboscopically engineer Hamiltonians with spatial features and periodicity below the diffraction limit of light used to create them by time-averaging over various configurations of a 1D optical Kronig–Penney (KP) lattice. The KP potential is a lattice of narrow subwavelength barriers spaced by half the optical wavelength (λ/2) and arises from the nonlinear optical response of the atomic dark state. Stroboscopic control over the strength and position of this lattice requires time-dependent adiabatic manipulation of the dark-state spin composition. We investigate adiabaticity requirements and shape our time-dependent light fields to respect the requirements. We apply this framework to show that a λ/4-spaced lattice can be synthesized using realistic experimental parameters as an example, discuss mechanisms that limit lifetimes in these lattices, explore candidate systems and their limitations, and treat adiabatic loading into the ground band of these lattices.

How to probe the microscopic onset of irreversibility with ultracold atoms

The microscopic onset of irreversibility is finally becoming an experimental subject. Recent experiments on microscopic open and even isolated systems have measured statistical properties associated with entropy production, and hysteresis-like phenomena have been seen in cold atom systems with dissipation (i.e. effectively open systems coupled to macroscopic reservoirs). Here we show how experiments on isolated systems of ultracold atoms can show dramatic irreversibility like cooking an egg. In our proposed experiments, a slow forward-and-back parameter sweep will sometimes fail to return the system close to its initial state. This probabilistic hysteresis is due to the same non-adiabatic spreading and ergodic mixing in phase space that explains macroscopic irreversibility, but realized without dynamical chaos; moreover this fundamental mechanism quantitatively determines the probability of return to the initial state as a function of tunable parameters in the proposed experiments. Matching the predicted curve of return probability will be a conclusive experimental demonstration of the microscopic onset of irreversibility.

Reaching the Continuum Limit in Finite-Temperature Ab Initio Field-Theory Computations in Many-Fermion Systems

Finite-temperature grand-canonical computations based on field theory are widely applied in areas including condensed matter physics, ultracold atomic gas systems, and the lattice gauge theory. However, these calculations have computational costs scaling as N_{s}^{3} with the size of the lattice or basis set, N_{s}. We report a new approach based on systematically controllable low-rank factorization that reduces the scaling of such computations to N_{s}N_{e}^{2}, where N_{e} is the average number of fermions in the system. In any realistic calculations aiming to describe the continuum limit, N_{s}/N_{e} is large and needs to be extrapolated effectively to infinity for convergence. The method thus fundamentally changes the prospect for finite-temperature many-body computations in correlated fermion systems. Its application, in combination with frameworks to control the sign or phase problem as needed, will provide a powerful tool in abinitio quantum chemistry and correlated electron materials. We demonstrate the method by computing exact properties of the two-dimensional Fermi gas with zero-range attractive interaction as a function of temperature in both the normal and superfluid states.