In addition to the conventional contribution that is directly controlled by the single-particle energy spectrum, the superfluid phase stiffness of a two-component Fermi gas has a geometric contribution that is governed by the quantum metric of the honeycomb's band structure. Here we take both contributions into account and construct phase diagrams for the critical superfluid transition temperature as a function of the chemical potential, particle filling, onsite interaction, and next-nearest-neighbor hopping. Our theoretical approach is based on a self-consistent solution of the BCS mean-field theory for the stationary Cooper pairs and the universal Berezinskii-Kosterlitz-Thouless (BKT) relation for the phase fluctuations.

In this paper, we discuss the possibility of building a linear cluster state based on modes with a certain orbital angular momentum. We show that in the system under consideration a field with a rich mode structure is generated in the cavity. We also analyze the conditions under which an infinite system of Heisenberg-Langevin equations describing the dynamics of intracavity fields can be shortened and solved analytically. To analyze the genuine number of quantum degrees of freedom, we use the supermodes technique. This approach allows us to build the most entangled cluster state.

The quasienergy band structure of an excitation in a regular lattice system is the spectral signature of the underlying lattice geometry. Here we study the formation of exotic quasienergy bandlike structures that follow not only from the lattice geometry alone, but also from the spatial characteristics of the excitation. The shape of the band structure associated with the excitation can be designed with features beyond what can be achieved by merely modifying the geometry of the regular lattice. These exotic spectral signatures are unstable and therefore of transient nature. The feasibility of observing this phenomenon in a simple setup consisting of a classical laser beam propagating along a regular array of evanescently coupled photonic nonlinear waveguides is discussed. We consider a honeycomb ribbon in which the transverse distribution for the laser beam is analyzed as a collective excitation.

Visual tracking (VT) is the process of locating a moving object of interest in a video. It is a fundamental problem in computer vision, with various applications in human-computer interaction, security and surveillance, robot perception, traffic control, etc. In this paper, we address this problem in the quantum setting, and present a quantum algorithm for VT based on the framework proposed by Henriques et al. [IEEE Trans. Pattern Anal. Mach. Intell. 7, 583 (2015)]. Our algorithm comprises two phases: training and detection. In the training phase, in order to discriminate the object and background, the algorithm trains a ridge regression classifier in the quantum state form where the optimal fitting parameters of ridge regression are encoded in the amplitudes. In the detection phase, the classifier is then employed to generate a quantum state whose amplitudes encode the responses of all the candidate image patches. The algorithm is shown to be polylogarithmic in scaling, when the image data matrices have low condition numbers, and therefore may achieve exponential speedup over the best classical counterpart. However, only quadratic speedup can be achieved when the algorithm is applied to implement the ultimate task of Henriques's framework, i.e., detecting the object position. We also discuss two other important applications related to VT: (1) object disappearance detection and (2) motion behavior matching, where much more significant speedup over the classical methods can be achieved. This work demonstrates the power of quantum computing in solving computer vision problems.

We present an efficient approach for dissipative generation of quantum superposition states in the microwave resonator, which is coupled to a superconducting qubit. We investigate the situation where the inversion symmetry of potential energy of the qubit is broken, and the strong two-photon nonlinear coupling between qubit and resonator can be realized via the transverse and longitudinal couplings. According to the two-photon dissipation and driving process, the dissipation of a qubit can be utilized to steer the microwave field into a quantum superposition of distinct coherent states, i.e., the Schrödinger cat state. In addition, we also extend the method to produce an entangled coherent state of two spatially separated resonators. Our scheme is based on quantum reservoir engineering and turns detrimental noise into a resource, which makes it feasible in experimental implementation. The present result may have potential applications in the field of quantum information processing with circuit QED systems.

We unravel some peculiar properties of ultra-long-range Rydberg molecules formed by an $s$-state ${}^{87}\mathrm{Rb}$ Rydberg atom and a corresponding ground-state atom whose electronic orbitals are spherically symmetric and therefore should not be influenced by the presence of weak magnetic fields. However, the electron-atom interaction, which establishes the molecular bond, is under certain conditions subject to a sizable spin-orbit coupling and, hence, sensitive to the magnetic field. This mechanism can be harnessed to counterintuitively align the $s$-state molecules with respect to the field axis. We demonstrate this by analyzing the angular-dependent Born-Oppenheimer potential energy surfaces and the supported vibrational molecular states. Our predictions open interesting possibilities for accessing the physics of relativistic electron-atom scattering experimentally.

We consider the formation of RbCs by an elliptically polarized laser pulse. By varying the ellipticity of the laser for sufficiently large laser intensity, we see that the formation probability presents a strong dependence, especially around ellipticity $1/\sqrt{2}$. We show that the analysis can be reduced to the investigation of the long-range interaction between the two atoms. The formation is mainly due to a small momentum shifts induced by the laser pulse. We analyze these results using the Silberstein expressions of the polarizabilities and show that the ellipticity of the field acts as a control knob for the formation probability, allowing significant variations of the dimer formation probability at a fixed laser intensity, especially in the region around an ellipticity of $1/\sqrt{2}$.

We investigate the formation of a Bose polaron when a single impurity in a Bose-Einstein condensate is quenched from a noninteracting to an attractively interacting state in the vicinity of a Feshbach resonance. We use a beyond-Fröhlich Hamiltonian to describe both sides of the resonance and a coherent-state variational ansatz to compute the time evolution of Boson density profiles in position space. We find that on the repulsive side of the Feshbach resonance, the Bose polaron performs long-lived oscillations, which is surprising given that the two-body problem has only one bound state coupled to a continuum. They arise due to interference between multiply occupied bound states and therefore can be only found with many-body approaches, such as the coherent-state ansatz. This is a distinguishing feature of the Bose polaron compared to the Fermi polaron, where the bound state can be occupied only once. We derive an implicit equation for the frequency of these oscillations and show that it can be approximated by the energy of the two-body bound state. Finally, we consider an impurity introduced at nonzero velocity and find that, on the repulsive side, it is periodically slowed down or even arrested before speeding up again.

We study the equilibrium properties of the repulsive quantum Bose-Hubbard model at high temperatures in arbitrary dimensions, with and without disorder. In its microcanonical setting the model conserves energy and particle number. The microcanonical dynamics is characterized by a pair of two densities: energy density $\varepsilon$ and particle number density $n$. The macrocanonical Gibbs distribution also depends on two parameters: the inverse non-negative temperature $\beta$ and the chemical potential $\mu$. We prove the existence of non-Gibbs states, that is, pairs $(\varepsilon ,n)$ which cannot be mapped onto $(\beta ,\mu )$. The separation line in the density control parameter space between Gibbs and non-Gibbs states $\varepsilon \sim n^2$ corresponds to infinite temperature $\beta =0$. The non-Gibbs phase cannot be cured into a Gibbs one within the standard Gibbs formalism using negative temperatures.

We study the Bloch oscillation dynamics of a spin-orbit-coupled cold atomic gas trapped inside a one-dimensional optical lattice. The eigenspectra of the system is identified as two interpenetrating Wannier-Stark ladders. Based on that, we carefully analyzed the Bloch oscillation dynamics and found out that intraladder coupling between neighboring rungs of the Wannier-Stark ladder give rise to ordinary Bloch oscillation, while interladder coupling leads to small-amplitude high-frequency oscillation superimposed on it. Specifically, spin-orbit interaction breaks Galilean invariance, which can be reflected by out-of-phase oscillation of the two spin components in the accelerated frame. The possibilities of generating spin current in this system are also explored.

We study relaxation dynamics in one-dimensional Bose gases, formulated as an initial value problem for the classical nonlinear Schrödinger equation. We propose an analytic technique which takes into account the exact spectrum of nonlinear modes that is both soliton excitations and dispersive continuum of radiation modes. Our method relies on the exact large-time asymptotics and uses the so-called dressing transformation to account for the solitons. The obtained results are quantitatively compared with the predictions of the linearized approach in the framework of the Bogoliubov theory. In the attractive regime, the interplay between solitons and radiation yields a damped oscillatory motion of the profile which resembles breathing. For the repulsive interaction, the solitons are confined in the sound cone region separated from the supersonic radiation.

We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample's refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known phase-retrieval problem in ptychography in a tomographic framework which allows for simultaneous reconstruction of the illumination function and the sample's refractive indices in three dimensions. Our iterative reconstruction algorithm is based on the Levenberg-Marquardt algorithm and we demonstrate the performance of our proposed method with simulated and real datasets.

The precise estimation of the gravitational acceleration is important for various disciplines. We consider making such an estimation using quantum optics. A Mach-Zehnder interferometer in an “optical fountain” type arrangement is considered and used to define a standard quantum limit for estimating the gravitational acceleration. We use an approach based on quantum field theory on a curved, Schwarzschild metric background to calculate the coupling between the gravitational field and the optical signal. The analysis is extended to include the injection of a squeezed vacuum to the Mach-Zehnder arrangement and also to consider an active, two-mode SU(1,1) interferometer in a similar arrangement. When detection loss is larger than $8\%$, the SU(1,1) interferometer shows an advantage over the MZ interferometer with single-mode squeezing input. The proposed system is based on current technology and could be used to examine the intersection of quantum theory and general relativity as well as for possible applications.

In a recent experiment [A. Vochezer, T. Kampschulte, K. Hammerer, and P. Treutlein, Phys. Rev. Lett. 120, 073602 (2018)], a novel kind of hybrid atom-optomechanical system has been realized by coupling atoms in a lattice to a membrane. While such a system promises a viable contender in the competitive field of simulating nonequilibrium many-body physics, its complete steady-state phase diagram is still lacking. Here we study the phase diagram of this hybrid system based on an atomic Bose-Hubbard model coupled to a quantum harmonic oscillator. We take both the expectation value of the bosonic operator and the mechanical motion of the membrane as order parameters and thereby identify four different quantum phases. Importantly, we find the atomic gas in the steady state of such a nonequilibrium setting undergoes a superfluid–Mott-insulator transition when the atom-membrane coupling is tuned to increase. Such a steady-state phase transition can be seen as the nonequilibrium counterpart of the conventional superfluid–Mott-insulator transition in the ground state of the Bose-Hubbard model. Further, no matter which phase the quantum gas is in, the mechanic motion of the membrane exhibits a transition from an incoherent vibration to a coherent one when the atom-membrane coupling increases, agreeing with the experimental observations. Our present study provides a simple way to study nonequilibrium many-body physics that is complementary to ongoing experiments on the hybrid atomic and optomechanical systems.

Locality imposes stringent constraints on the spreading of information in nonrelativistic quantum systems, which is reminiscent of a “light cone,” a causal structure arising in their relativistic counterparts. Long-range interactions can potentially soften such constraints, allowing almost instantaneous long jumps of particles, into the “spacelike” region, thus defying causality. Since interactions decaying as a power law with distance $r^{-\alpha }$ are ubiquitous in nature, it is pertinent to understand what is the fate of causality and information spreading in such systems. Using a numerically exact technique we address these questions by studying the out-of-time-order correlation function of a representative generic system in one dimension. We show that while the interactions are long range, their effect on information spreading is asymptotically negligible as long as $\alpha >1$. In this range we find a complex compound behavior, where, after a short transient, a fully local behavior emerges, yielding asymptotic light cones virtually indistinguishable from light cones in corresponding local models. The long-range nature of the interaction is only expressed in the power-law leaking of information from the light cone, with the same exponent as the exponent of the interaction $\alpha$. Our results directly apply also to corresponding response functions and suggest that previously obtained rigorous bounds on information spreading in long-range interacting systems are not tight, and could be potentially improved.

The arrival-time problem for the free particle in one dimension may be formulated as the problem of determining a joint probability for the particle being found on opposite sides of the $x$ axis at two different times. We explore this problem using a two-time quasiprobability linear in the projection operators, a natural counterpart of the corresponding classical problem. We show that it can be measured either indirectly, by measuring its moments in different experiments, or directly, in a single experiment using a pair of sequential measurements in which the first measurement is weak (or, more generally, ambiguous). We argue that when positive, it corresponds to a measurement-independent arrival-time probability. For small time intervals it coincides approximately with the time-averaged current, in agreement with semiclassical expectations. The quasiprobability can be negative and we exhibit a number of situations in which this is the case. We interpret these situations as the presence of “quantumness,” in which the arrival-time probability is not properly defined in a measurement-independent manner. Backflow states, in which the current flows in the direction opposite to the momentum, are shown to provide an interesting class of examples such situations. We also show that the quasiprobability is closely linked to a set of two-time Leggett-Garg inequalities, which test for macroscopic realism.

Quantum communication protocols are typically formulated in terms of abstract qudit states and operations, leaving the question of an experimental realization open. Direct translations of these protocols, say, into single photons with some $d$-dimensional degree of freedom, are typically challenging to realize. Multimode coherent states, on the other hand, can be easily generated experimentally. Reformulation of protocols in terms of these states has been a successful strategy for implementation of quantum protocols. Quantum key distribution and the quantum fingerprinting protocol have both followed this route. In this paper, we characterize the Gram matrices of multimode coherent states in an attempt to understand the class of communication protocols which can be implemented using these states. As a side product, we are able to use this characterization to show that the Hadamard exponential of a Euclidean distance matrix is positive semidefinite. We also derive the closure of the Gram matrices, which can be implemented in this way, so that we also characterize those matrices, which can be approximated arbitrarily well using multimode coherent states.