Ground-state properties of a few attractively interacting ultracold atoms of different mass confined in a one-dimensional harmonic trap are studied. The analysis is performed in terms of the noise correlation, which captures the two-particle correlations induced by the mutual interactions. Depending on the mass ratio between the components' atoms, the interparticle correlations change their properties significantly from a strong pairlike correlation to an almost uncorrelated phase. This change is accompanied by a simultaneous change in the structure of the many-body ground state. A crucial role of the quantum statistics is emphasized by comparing properties of the Fermi-Fermi mixture with a corresponding Fermi-Bose system.

We study the supercurrent decay of a Bose-Einstein condensate in a ring trap combined with a repulsive barrier potential. In recent experiments, Kumar et al. [Phys. Rev. A 95, 021602(R) (2017)] have measured the dependence of the decay rate on the temperature and the barrier strength. However, the origin of the decay observed in the experiment remains unclear. We calculate the rate of supercurrent decay due to thermally activated phase slips (TAPS) by using the Kramers formula based on the Gross-Pitaevskii mean-field theory. The resulting decay rate is astronomically small compared to that measured in the experiment, thus excluding the possibility of TAPS as the decay mechanism. Alternatively, we argue that three-body losses can be relevant to the observed decay and predict that one can observe supercurrent decay via TAPS by decreasing the number of atoms.

Unique and highly tunable optical properties of $\mathcal{PT}$-symmetric systems and metamaterials enable a plenty of entirely new linear and nonlinear optical phenomena with numerous applications, e.g., for designing subdiffraction lenses, nonreciprocal devices, etc. Therefore, the artificial media with the $\mathcal{PT}$ symmetry attract ever-increasing attention and are now a subject for intensive investigations. One of the commonly used methods providing information about the optical response of artificial nanostructural media is a so-called effective medium theory. Here we examine the possibility of utilizing the effective medium theory for a comprehensive analysis of $\mathcal{PT}$-symmetric multilayered systems composed of alternating loss and gain slabs. We show that applicability of local effective material parameters (or Maxwell Garnett approximation) is very limited and cannot be exploited for a prediction of exceptional points marking a $\mathcal{PT}$ symmetry breaking. On the other hand, nonlocal bianisotropic effective medium parameters can be reliably used, if the thickness of a unit cell is much smaller than the radiation wavelength. In the case of obliquely incident plane waves, we reveal the limitation on the loss-gain coefficient, which should not be too large compared with the real part of the permittivity. We believe that our findings can improve the fundamental understanding of physics behind $\mathcal{PT}$-symmetric systems and advance the development of auxiliary tools for analyzing their peculiar optical response.

We propose a simple quasi-phase-matching (QPM) scheme in high-order harmonic generation (HHG) based on the approximately linear dependence of the phase mismatch on harmonic order. With this scheme, essentially all the harmonic orders are phase matched simultaneously, with harmonic order $q$ experiencing a $q\mathrm{th}$-order QPM. We validate this proposal by simulations using a semiclassical numerical model of HHG.

In a driven cavity QED system with two nonidentical qubits of different resonant frequencies, a multiphoton nonclassical state can be generated by single-photon and two-photon cavity-induced transparency (CIT). Due to the existence of the quasi-subradiant state, the parameter of radiance witness $R$ can be greater than unity, which demonstrates that the cavity QED system is in the hyperradiance regime. In this hyperradiance regime, although the second-order correlation function $g^{\left(2\right)}\left(0\right)$ is greater than unity, the photon statistics still exhibits the higher-order sub-Poissonian distribution. Because the single-photon and two-photon processes are suppressed by CIT-like effects, the three-photon process is enhanced, which leads to Klyshko's criterion $K_n<1$ for $n>2$, indicating the appearance of multiphoton nonclassicality. Based on this principle, we propose a scheme for preparing multiphoton nonclassical light with a three-photon probability of ${10}^{-4}$, which is feasible for experiment.

Structured illumination allows for satisfying the first Kerker condition of in-phase perpendicular electric and magnetic dipole moments in any isotropic scatterer that supports electric and magnetic dipole resonances. The induced Huygens' dipole may be utilized for unidirectional coupling to waveguide modes that propagate transverse to the excitation beam. We study two configurations of a Huygens' dipole, longitudinal electric and transverse magnetic dipole moments or vice versa. We experimentally show that only the radially polarized emission of the first and azimuthally polarized emission of the second configuration are directional in the far field. This polarization selectivity implies that directional excitation of either transverse magnetic (TM) or transverse electric (TE) waveguide modes is possible. Applying this concept to a single dielectric nanoantenna excited with structured light, we are able to experimentally achieve scattering directivities of around 23 and 18 dB in TM and TE modes, respectively. This strong directivity paves the way for tunable polarization-controlled nanoscale light routing and applications in optical metrology, localization microscopy, and on-chip optical devices.

The resource theory of thermal operations aims at describing possible transitions of microscale systems interacting with a macroscale environment under the fundamental assumption of energy conservation. For initial quantum states diagonal in the basis of the local Hamiltonian, these transitions are completely described by thermal processes (TPs), which form a convex set. In this paper, we give a complete characterization of the set of states that can be achieved through TPs, by describing the boundary of the allowed set of states using the so-called thermomajorization curves as a tool. We address the problem of achieving a certain transition through a convex combination of products of extremal TPs. We characterize all extremal TPs by associating them with transportation matrices. It becomes evident that there are extremal TPs that are not required in the implementation of any transition allowed by TPs. The statement holds for every dimension $d\ge 4$ of the state space. A property of the associated graphs, biplanarity, is identified as the distinguishing feature of these extremal TPs that are required for the arbitrary transition allowed by TPs.

Non-Hermitian systems exhibit many peculiar dynamic behaviors that never showed up in Hermitian systems. The existence of spectral singularity for a non-Hermitian scattering center provides a “lasing mechanism” in the context of quantum mechanics. In this paper, we investigate the dynamics of the non-Hermitian Su-Schrieffer-Heeger model around an exceptional point, based on an analysis of parity-time and chiral-time symmetries of the Hamiltonian. We show exactly that a finite system near its exceptional point can support EP-related amplification of cyclic states. It becomes a stationary laser solution with linear-power amplification under certain conditions in an infinite limit. In contrast to the SS lasing mechanism for a scattering system, such an SSH chain acts as an active laser medium at threshold, within which a stationary particle emission can be fired anywhere, rather than a specific location at the non-Hermitian scattering center only. In addition, some relevant peculiar phenomena arising from interference between wave packets are revealed based on the analytical solutions.

We propose an efficient approach for the generation of a stable entangled state of microwave fields in circuit quantum electrodynamics. The system under consideration consists of two linearly coupled superconducting resonators, each of which is coupled to a superconducting flux qubit. By individually driving the qubits to engineer the desired interactions with the resonators, we show that the energy relaxation of qubits can be exploited to steer the two resonators into the two-mode entangled state via a dissipative dynamical process. Since our protocol is based on quantum reservoir engineering, neither specific initialization nor unitary dynamics is required. Moreover, the distinct advantage of our scheme is that the quantum state preparation is robust in relation to inhomogeneous parameters, i.e., there is no need for identical qubit-field couplings, as well as the same resonance frequencies of the resonators. These features make the present scheme pretty feasible for experimental implementation.

A quantum error correction (QEC) code uses $N_{\mathrm{c}}$ quantum bits to construct one “logical” quantum bit of better quality than the original “physical” ones. QEC theory predicts that the failure probability $p_L$ of logical qubits decreases exponentially with $N_{\mathrm{c}}$ provided the failure probability $p$ of the physical qubit is below a certain threshold $p<p_{\mathrm{th}}$. In particular, QEC theorems imply that the logical qubits can be made arbitrarily precise by simply increasing $N_c$. In this article, we search for physical mechanisms that lie outside of the hypothesis of QEC theorems and set a limit ${\eta }_{\mathrm{L}}$ to the precision of the logical qubits (irrespectively of $N_c$). ${\eta }_{\mathrm{L}}$ directly controls the maximum number of operations $\propto 1/{\eta }_{\mathrm{L}}^2$ that can be performed before the logical quantum state gets randomized, hence the depth of the quantum circuits that can be considered. We identify a type of error—silent stabilizer failure—as a mechanism responsible for finite ${\eta }_{\mathrm{L}}$ and discuss its possible causes. Using the example of the topological surface code, we show that a single local event can provoke the failure of the logical qubit, irrespectively of $N_c$.

We characterize nonselective global projective measurements capable of increasing quantum entanglement between two particles. In particular, by choosing negativity to quantify entanglement, we show that entanglement of any pure nonmaximally entangled state can be improved in this way (but not of any mixed state) and we provide detailed analysis for two qubits. It is then shown that Markovian open system dynamics can only approximate such measurements, but this approximation converges exponentially fast as illustrated using the Araki-Żurek model. We conclude with numerical evidence that macroscopic bodies in a random pure state do not gain negativity in a random nonselective global measurement.

We analytically and numerically investigate the steady-state entanglement and coherence of two coupled qubits, each interacting with a local boson or fermion reservoir, based on the Bloch-Redfield master equation beyond the secular approximation. We find that there is nonvanishing steady-state coherence in the nonequilibrium scenario, which grows monotonically with the nonequilibrium condition quantified by the temperature difference or chemical potential difference of the two baths. The steady-state entanglement, in general, is a nonmonotonic function of the nonequilibrium condition as well as the bath parameters in the equilibrium setting. We also discover that weak interqubit coupling and high base temperature or chemical potential of the baths can strongly suppress the steady-state entanglement and coherence, regardless of the strength of the nonequilibrium condition. On the other hand, the energy detuning of the two qubits, when used in a compensatory way with the nonequilibrium condition, can lead to significant enhancement of the steady-state entanglement in some parameter regimes. In addition, the qubits typically have a stronger steady-state entanglement when coupled to fermion baths exchanging particles with the system than boson baths exchanging energy with the system, under similar conditions. We also identify a close connection between the energy current flowing through the system and the steady-state coherence. Preliminary investigations suggest that these results are insensitive to the form of the reservoir spectral densities in the Markovian regime. Feasible experimental realization of measuring the steady-state entanglement and coherence is discussed for the coupled qubit system in nonequilibrium environments. Our findings offer some general guidelines for optimizing the steady-state entanglement and coherence in the coupled qubit system and may find potential applications in quantum information technology.

We introduce an approximation for strong-laser-field-induced ionization of atoms, which we call atom-Volkov strong-field approximation (aV SFA). For the final state, instead of a plane wave (used in the standard well-known SFA) or a Coulomb wave (used in the Coulomb-Volkov SFA), in the aV SFA we use the exact atom-specific scattering states. We first introduce the aV SFA as an ansatz and show that it yields results that are closer to the exact results than those obtained using the SFA. After that, we systematically derive an iterative theory whose zeroth order is equal to the introduced aV SFA. We analyze its first-order correction, which corresponds to electron rescattering off the parent ion and show that, in the case of forward scattering, this correction leads to the low-energy structures in the photoelectron spectra which are observed in the experiments.

Non-Hermitian systems having parity-time ($\mathcal{PT}$) symmetry can undergo a transition, spontaneously breaking the symmetry. Ultracold atomic gases provide an ideal platform to study interaction effects on the transition. We consider a model system of $N$ bosons of two components confined in a tight trap. Radio-frequency and laser fields are coupled to the bosons such that the single-particle Non-Hermitian Hamiltonian $h_{\mathcal{P}T}=-i\mathrm{\Gamma }{\sigma }_z+J{\sigma }_x$, which has $\mathcal{PT}$ symmetry, can be simulated in a passive way, namely, in the physical system there is only incurred atom loss but no gain. We show that when interatomic interactions are tuned to maintain the symmetry, the $\mathcal{PT}$-symmetry-breaking transition is affected only by the SU(2) variant part of the interatomic interactions. We find that the transition point ${\mathrm{\Gamma }}_{\mathrm{tr}}$ decreases as the strength of this interaction part or $N$ increases; in the strong strength limit for this interaction part, ${\mathrm{\Gamma }}_{\mathrm{tr}}$ scales as the strength to the power of $-(N-1)$. We also give signatures of the $\mathcal{PT}$-symmetric and the symmetry-breaking phases for the interacting bosons in experiment.

Ultracold atoms in optical lattices form a clean quantum simulator platform which can be utilized to examine topological phenomena and test exotic topological materials. Here we propose an experimental scheme to measure the Chern numbers of two-dimensional multiband topological insulators with bosonic atoms. We show how to extract the topological invariants out of a sequence of time-of-flight images by applying a phase-retrieval algorithm to matter waves. We illustrate advantages of using bosonic atoms as well as efficiency and robustness of the method with two prominent examples: the Harper-Hofstadter model with an arbitrary commensurate magnetic flux and the Haldane model on a brick-wall lattice.

We analyze two-time correlators as the most natural characteristic of a propagating quadrature-squeezed field in the transient regime. The considered system is a parametrically driven resonator with a time-dependent drive. Using a semiclassical approach derived from the input-output theory, we develop a technique for calculation of the two-time correlators, which are directly related to fluctuations of the measured integrated signal. While in the steady state the correlators are determined by three parameters (as for the phase-space ellipse describing a squeezed state), four parameters are necessary in the transient regime. The formalism can be generalized to weakly nonlinear resonators with additional coherent drive. We focus on squeezed microwave fields relevant to the measurement of superconducting qubits; however, our formalism is also applicable to optical systems. The results can be readily verified experimentally.

The spontaneous emission of a V-type three-level quantum emitter near graphene layers is investigated. With appropriate doping densities, graphene layers support transverse electric- (TE-) polarized surface plasmons. This kind of plasmon can enhance the decay rates of dipoles parallel to the layers, and subsequently, strong quantum interference presents between the two orthogonal transition dipoles of the emitter. As a result, the emission field polarization and the spectrum can be radically changed. This can be evidence of the TE-polarized surface plasmons in the graphene layers.

Non-Markovian quantum processes exhibit different memory effects when measured in different ways; an unambiguous characterization of memory length requires accounting for the sequence of instruments applied to probe the system dynamics. This instrument-specific notion of quantum Markov order displays stark differences to its classical counterpart. Here, we explore the structure of quantum stochastic processes with finite memory length in detail. We begin by examining a generalized collision model with memory, before framing this instance within the general theory. We detail the constraints that are placed on the underlying system-environment dynamics for a process to exhibit finite Markov order with respect to natural classes of probing instruments, including deterministic (unitary) operations and sequences of generalized quantum measurements with informationally complete repreparations. Lastly, we show how processes with vanishing quantum conditional mutual information form a special case of the theory. Throughout, we provide a number of representative, pedagogical examples to display the salient features of memory effects in quantum processes.

The reduced $k$-particle density matrix of a density matrix on finite-dimensional, fermion Fock space can be defined as the image under the orthogonal projection in the Hilbert-Schmidt geometry onto the space of $k$-body observables. A proper understanding of this projection is therefore intimately related to the representability problem, a long-standing open problem in computational quantum chemistry. Given an orthonormal basis in the finite-dimensional one-particle Hilbert space, we explicitly construct an orthonormal basis of the space of Fock space operators which restricts to an orthonormal basis of the space of $k$-body operators for all $k$.

We demonstrate a method to obtain the spectra of $1/f$ noises in spin-qubit devices from randomized benchmarking, assisted by supervised learning. The noise exponent, which indicates the correlation within the noise, is determined by training a double-layer neural network with the ratio between the randomized benchmarking results of pulse sequences that correct noise or not. After the training is completed, the neural network is able to predict the exponent within an absolute error of about 0.05, comparable with existing methods. The noise amplitude is then evaluated by training another neural network with the decaying fidelity of randomized benchmarking results from the uncorrected sequences. The relative error for the prediction of the noise amplitude is as low as 5% provided that the noise exponent is known. Our results suggest that the neural network is capable of predicting noise spectra from randomized benchmarking, which can be an alternative method to measure noise spectra in spin-qubit devices.