Search

Synthetically spin-orbit coupling in cold atoms couples the pseudo-spin and spatial degrees of freedom, and therefore the inherent spin symmetry of the system plays an important role. In systems of two pseudo-spin degrees, two particles configure symmetric states and anti-symmetric states, but the spin symmetry can be mixed for more particles. We study the role of mixed spin symmetry in the presence of spin-orbit coupling and consider the system of three bosons with two hyper-fine states trapped in a harmonic potential. We investigate the ground state and the energy spectrum by implementing exact diagonalization. It is found that the interplay between spin-orbit coupling and repulsive interactions between anti-aligned pseudo-spins increases the population of the unaligned spin components in the ground state. The emergence of the mixed spin symmetric states compensates for the rise of the interaction energy. With the aligned interaction on, the avoided crossing between the ground state and the first excited state is observed only for small interaction, and this causes shape changes in the spin populations. Furthermore, we find that the pair correlation of the ground state shows similarly to that of Tonks-Girardeau gas even for relatively small contact interactions and such strong interaction feature is enhanced by the spin-orbit coupling., Comment: 10 pages, 9 figures

Local Hamiltonians, $H_k$, describe non-trivial $k$-body interactions in quantum many-body systems. Here, we address the dynamical simulatability of a $k$-local Hamiltonian by a simpler one, $H_{k'}$, with $k'2$ increases with $k$. Finally, we propose a method to search for the $k'$-local Hamiltonian that simulates, with the highest possible precision, the short time dynamics of a given $H_k$ Hamiltonian., Comment: 13 pages, 6 figures, accepted version for publication

Based on exact integration of the Schr\"odinger equation, we numerically study microscopic contributions to the entropy production for the single electron transistor, a paradigmatic model describing a single Fermi level tunnel coupled to two baths of free fermions. To this end, we decompose the entropy production into a sum of information theoretic terms and study them across all relevant time scales, including the nonequilibrium steady state regime and the final stage of global thermalization. We find that the entropy production is dominated for most times by microscopic deviations from thermality in the baths and the correlation between (but not inside) the baths. Despite these microscopic deviations from thermality, the temperatures and chemical potentials of the baths thermalize as expected, even though our model is integrable. Importantly, this observation is confirmed for both initially mixed and pure states. We further observe that the bath-bath correlations are quite insensitive to the system-bath coupling strength contrary to intuition. Finally, the system-bath correlation, small in an absolute sense, dominates in a relative sense and displays pure quantum correlations for all studied parameter regimes., Comment: 12 pages, 9 figures

Entanglement measures quantify nonclassical correlations present in a quantum system, but can be extremely difficult to calculate, even more so, when information on its state is limited. Here, we consider broad families of entanglement criteria that are based on variances of arbitrary operators and analytically derive the lower bounds these criteria provide for two relevant entanglement measures: the best separable approximation (BSA) and the generalized robustness (GR). This yields a practical method for quantifying entanglement in realistic experimental situations, in particular, when only few measurements of simple observables are available. As a concrete application of this method, we quantify bipartite and multipartite entanglement in spin-squeezed Bose-Einstein condensates of $\sim 500$ atoms, by lower bounding the BSA and the GR only from measurements of first and second moments of the collective spin operator., Comment: Comments are welcome

Quantum thermodynamics often deals with the dynamics of small quantum machines interfacing with a large and complex environment. Virtual qubits, collisional models and reset master equations have become highly useful tools for predicting the qualitative behaviour of two-dimensional target systems coupled to few-qubit machines and a thermal environment. While few successes in matching the simplified model parameters for all possible physical systems are known, the qualitative predictions still allow for a general design of quantum machines irrespective of the implementation. We generalise these tools by introducing multiple competing virtual qubits for modelling multi-dimensional systems coupled to larger and more complex machines. By simulating the full physical dynamics for targets with three dimensions, we uncover general properties of reset models that can be used as `dials' to correctly predict the qualitative features of physical changes in a realistic setup and thus design autonomous quantum machines beyond a few qubits. We then present a general analytic solution of the reset model for arbitrary-dimensional systems coupled to multi-qubit machines. Finally, we showcase an improved three-level laser as an exemplary application of our results., Comment: 9+6 pages, 6 figures

Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no initial information about the parameter value is available, e.g., when few measurements are performed. Here, we consider three paradigmatic estimation schemes in continuous-variable quantum metrology (estimation of displacements, phases, and squeezing strengths) and analyse them from the Bayesian perspective. For each of these scenarios, we investigate the precision achievable with single-mode Gaussian states under homodyne and heterodyne detection. This allows us to identify Bayesian estimation strategies that combine good performance with the potential for straightforward experimental realization in terms of Gaussian states and measurements. Our results provide practical solutions for reaching uncertainties where local estimation techniques apply, thus bridging the gap to regimes where asymptotically optimal strategies can be employed., Comment: 16+4 pages, 8 figures

We develop a framework and give an example for situations where two distinct Hamiltonians living in the same Hilbert space can be used to simulate the same physics. As an example of an analog simulation, we first discuss how one can simulate an infinite-range-interaction one-axis twisting Hamiltonian using a short-range nearest-neighbor-interaction Heisenberg XXX model with a staggered field. Based on this, we show how one can build an alternative version of a digital quantum simulator. As a by-product, we present a method for creating many-body maximally entangled states using only short-range nearest-neighbor interactions., Comment: 5 pages, 3 figures

We explore the influence of contact interactions on a synthetically spin-orbit coupled system of two ultracold trapped atoms. Even though the system we consider is bosonic, we show that a regime exists in which the competition between the contact and spin-orbit interactions results in the emergence of a ground state that contains a significant contribution from the anti-symmetric spin state. This ground state is unique to few-particle systems and does not exist in the mean-field regime. The transition to this state is signalled by an inversion in the average momentum from being dominated by centre-of-mass momentum to relative momentum and also affects the global entanglement shared between the real- and pseudo-spin spaces. Indeed, competition between the interactions can also result in avoided crossings in the groundstate which further enhances these correlations. However, we find that correlations shared between the pseudo-spin states are strongly depressed due to the spin-orbit coupling and therefore the system does not contain spin-spin entanglement., Comment: 21 pages, 9 figures

We study a two-level impurity coupled locally to a quantum gas on an optical lattice. For state-dependent interactions between the impurity and the gas, we show that its evolution encodes information on the local excitation spectrum of gas at the coupling site. Based on this, we design a nondestructive method to probe the system's excitations in a broad range of energies by measuring the state of the probe using standard atom optics methods. We illustrate our findings with numerical simulations for quantum lattice systems, including realistic dephasing noise on the quantum probe, and discuss practical limits on the probe dephasing rate to fully resolve both regular and chaotic spectra., Comment: 17 single-column pages, 4 figures. Matches published version

We investigate the dynamics of the rate function and of local observables after a quench in models which exhibit phase transitions between a superfluid and an insulator in their ground states. Zeros of the return probability, corresponding to singularities of the rate functions, have been suggested to indicate the emergence of dynamical criticality and we address the question of whether such zeros can be tied to the dynamics of physically relevant observables and hence order parameters in the systems. For this we first numerically analyze the dynamics of a hard-core boson gas in a one-dimensional waveguide when a quenched lattice potential is commensurate with the particle density. Such a system can undergo a pinning transition to an insulating state and we find non-analytic behavior in the evolution of the rate function which is indicative of dynamical phase transitions. In addition, we perform simulations of the time dependence of the momentum distribution and compare the periodicity of this collapse and revival cycle to that of the non-analyticities in the rate function: the two are found to be closely related only for deep quenches. We then confirm this observation by analytic calculations on a closely related discrete model of hard-core bosons in the presence of a staggered potential and find expressions for the rate function for the quenches. By extraction of the zeros of the Loschmidt amplitude we uncover a non-equilibrium timescale for the emergence of non-analyticities and discuss its relationship with the dynamics of the experimentally relevant parity operator., Comment: 8 pages, 6 figures, minor changes and some references added

We show theoretically that periodic density patterns are stabilized in two counter-propagating Bose-Einstein condensates of atoms in different hyperfine states under Rabi coupling. In the presence of coupling, the relative velocity between two components is localized around density depressions in quasi-one-dimensional systems. When the relative velocity is sufficiently small, the periodic pattern reduces to a periodic array of topological solitons as kinks of relative phase. According to our variational and numerical analyses, the soliton solution is well characterized by the soliton width and density depression. We demonstrate the dependence of the depression and width on the Rabi frequency and the coupling constant of inter-component density-density interactions. The periodic pattern of the relative phase transforms continuously from a soliton array to a sinusoidal pattern as the period becomes smaller than the soliton width. These patterns become unstable when the localized relative velocity exceeds a critical value. The stability-phase diagram of this system is evaluated with a stability analysis of countersuperflow, by taking into account the finite-size-effect owing to the density depression., Comment: 9 pages, 8 figures