We examine the stability and dynamics of a family of crossed dark solitons in a harmonically confined Bose-Einstein condensate in two dimensions. Working in a regime where the fundamental snake instability is suppressed, we show the existence of an instability which leads to an interesting collapse and revival of the initial state for the fundamental case of two crossed solitons. The instability originates from the singular point where the solitons cross, and we characterize it by examining the Bogoliubov spectrum. Finally, we extend the treatment to systems of higher symmetry.

We explore the dynamics of a Bose gas following its quench to a strongly interacting regime near a Feshbach resonance. Within a self-consistent Bogoliubov analysis we find that after the initial condensate-quasiparticle Rabi oscillations, at long time scales the gas is characterized by a nonequilibrium steady-state momentum distribution function, with depletion, condensate density, and contact that deviate strongly from their corresponding equilibrium values. These are in a qualitative agreement with recent experiments on ${}^{85}$Rb by Makotyn et al. Our analysis also suggests that for sufficiently deep quenches close to the resonance the nonequilibrium state undergoes a phase transition to a fully depleted state, characterized by a vanishing condensate density.

We study a stability criterion hypothesis for superfluids expressed in terms of the local density spectral function ${\mathcal{I}}_n(\mathbf{r},\omega )$ that is applicable to both homogeneous and inhomogeneous systems. We evaluate the local density spectral function in the presence of a one-dimensional repulsive or attractive external potential within Bogoliubov theory, using solutions for the tunneling problem. We also evaluate the local density spectral function using an orthogonal basis, and calculate the autocorrelation function $C_n(\mathbf{r},t)$. When superfluids in a $d$-dimensional system flow below a threshold, ${\mathcal{I}}_n(\mathbf{r},\omega )\propto {\omega }^d$ holds in the low-energy regime and $C_n(\mathbf{r},t)\propto 1/t^{d+1}$ holds in the long-time regime. However, when superfluids flow with the critical current, ${\mathcal{I}}_n(\mathbf{r},\omega )\propto {\omega }^{\beta }$ holds in the low-energy regime and $C_n(\mathbf{r},t)\propto 1/t^{\beta +1}$ holds in the long-time regime with $\beta <d$. These results support the stability criterion hypothesis recently proposed.

To explore superfluidity in flat-band systems, we consider a Bose-Hubbard model on a cross-linked ladder with $\pi$ flux, which has a flat band with a gap between the other band for noninteracting particles, where we study the effect of the on-site repulsion nonperturbatively. For low densities, we find exact degenerate ground states, each of which is a Wigner solid with nonoverlapping Wannier states on the flat band. At higher densities, the many-body system, when projected onto the lower flat band, can be mapped to a spin-chain model. This mapping enables us to reveal the existence of a Tomonaga-Luttinger liquid comprising pairs of bosons. Interestingly, the high- and low-density regions have an overlap, where the two phases coexist.

We report a measurement of the condensation energy of a two-component Fermi gas with tunable interactions. From the equation of state of the gas, we infer the properties of the normal phase in the zero-temperature limit. By comparing the pressure of the normal phase at $T=0$ to that of the low-temperature superfluid phase, we deduce the condensation energy, i.e., the energy gain of the system upon being in the superfluid rather than the normal state. We compare our measurements to a ladder approximation description of the normal phase and to a fixed-node Monte Carlo approach, finding excellent agreement. We discuss the relationship between condensation energy and pairing gap in the BEC-BCS crossover.

We demonstrate both theoretically and experimentally that a finite Airy beam changes its trajectory and shape in optically induced waveguide arrays consisting of different kinds of defects. The propagation dynamics and beam acceleration are controlled with positive and negative defects, and appropriate refractive index change. An additional class of discrete beams and Airy defect modes are demonstrated.

A class of nonparaxial accelerating optical waves is introduced. These are beams with a Bessel-like profile that are capable of shifting laterally along fairly arbitrary trajectories as the wave propagates in free space. The concept expands on our previous proposal of paraxial accelerating Bessel-like beams to include beams with subwavelength lobes and/or large trajectory angles. Such waves are produced when the phase at the input plane is engineered so that the interfering ray cones are made to focus along the prespecified path. When the angle of these cones is fixed, the beams possess a diffraction-free Bessel profile on planes that stay normal to their trajectory, which can be considered as a generalized definition of diffractionless propagation in the nonparaxial regime. The analytical procedure leading to these results is based on a ray-optics interpretation of Rayleigh-Sommerfeld diffraction and is presented in detail. The evolution of the proposed waves is demonstrated through a series of numerical examples and a variety of trajectories.

Single-photon coherent optics represents a fundamental importance for the investigation of quantum light-matter interactions. While most work has considered the interaction in the steady-state regime, here we demonstrate that a single-photon pulse shorter than any relaxation time in a medium propagates without energy loss and is consistently transformed into a zero-area pulse. A general analytical solution is found for photon passage through a cold ensemble of $\Lambda$-type atoms confined inside a hollow core of a single-mode photonic-crystal fiber. We use the robust far-off-resonant Raman scheme to control the pulse reshaping by an intense control laser beam and show that in the case of cw control field, for exact two-photon resonance, the outgoing photon displays an oscillating temporal distribution, which is the quantum counterpart of a classical field ringing, while for nonzero two-photon detuning a slow photon is produced. We demonstrate also that a train of readout control pulses coherently recalls the stored photon in many well-separated temporal modes, thus producing time-bin entangled single-photon states. Such states, which allow sharing quantum information among many users, are highly demanded for applications in long-distance quantum communication.

Universal quantum computation can be achieved by simply performing single-spin measurements on a highly entangled resource state, such as cluster states. The family of Affleck-Kennedy-Lieb-Tasaki (AKLT) states has recently been explored; for example, the spin-1 AKLT chain can be used to simulate single-qubit gate operations on a single qubit, and the spin-3/2 two-dimensional AKLT state on the honeycomb lattice can be used as a universal resource. However, it is unclear whether such universality is a coincidence for the specific state or a shared feature in all two-dimensional AKLT states. Here we consider the family of spin-3/2 AKLT states on various trivalent Archimedean lattices and show that in addition to the honeycomb lattice, the spin-3/2 AKLT states on the square octagon $(4,8^2)$ and the “cross” $(4,6,12)$ lattices are also universal resource, whereas the AKLT state on the “star” $(3,{12}^2)$ lattice is likely not due to geometric frustration.

We consider the problem of calculating the logical error probability for a stabilizer quantum code subject to random Pauli errors. To access the regime of large code distances where logical errors are extremely unlikely we adopt the splitting method widely used in Monte Carlo simulations of rare events and Bennett's acceptance ratio method for estimating the free energy difference between two canonical ensembles. To illustrate the power of these methods in the context of error correction, we calculate the logical error probability $P_L$ for the two-dimensional surface code on a square lattice with a pair of holes for all code distances $d\le 20$ and all error rates $p$ below the fault-tolerance threshold. Our numerical results confirm the expected exponential decay $P_L\sim \exp [-\alpha (p\left)d\right]$ and provide a simple fitting formula for the decay rate $\alpha \left(p\right)$. Both noiseless and noisy syndrome readout circuits are considered.

Heisenberg-type spin models in the limit of a low number of excitations are useful tools to study basic mechanisms in strongly correlated and magnetic systems. Many of these mechanisms can be experimentally tested using ultracold atoms. Here, we discuss the implementation of a quantum state transfer protocol in a tight-binding chain in the presence of an inhomogeneous external potential. We show that it can be used to extend the parameter range in which high-fidelity state transfer can be achieved beyond the well established weak-coupling regime. Among the class of mirror-reflecting potentials that allow for high fidelity quantum state transfer, the harmonic case is especially relevant because it allows us to formulate a proposal for the experimental implementation of the protocol in the context of optical lattices.

We present both experimental and theoretical results for the dissociative ionization of ${\mathrm{D}}_2$ molecules induced by electron impact. Cross sections are determined in the molecular frame and are fully differential in the energies and emission angles of the dissociation fragments. Transitions are considered from the $X$${}^1{\Sigma }_g{}^{+}$ electronic ground state of D${}_2$ to the $2s{\sigma }_g$, $2p{\pi }_u$ and $2p{\sigma }_u$ excited states of D${}_2{}^{+}$. The experimental results are compared to calculations performed within the molecular four-body distorted-wave framework to describe the multicenter nature of the scattering process. The cross sections reveal a dramatic dependence on both the alignment of the internuclear axis with respect to the direction of the projectile momentum and on the symmetry of the excited dissociating state which is energetically resolved.

We study first-order spatial coherence for interacting polar bosons trapped in triple-well potentials. It is argued that besides the well-known coherence produced by couplings related to tunneling between the sites, there exists a nonlocal coherence predominantly determined by intersite interactions, which prevails between the outer sites of the triple well when their total filling is odd. We find that the nonlocal interaction-induced coherence originates from the superposition of degenerate many-body states in symmetric triple wells, and demonstrate its robustness against perturbations due to various tunneling mechanisms and thermal fluctuations.

We investigate the sensitivity with which the temperature and the chemical potential characterizing quantum gases can be measured. We calculate the corresponding quantum Fisher information matrices for both fermionic and bosonic gases. For the latter, particular attention is devoted to the situation close to the Bose-Einstein condensation transition, which we examine not only for the standard scenario in three dimensions, but also for generalized condensation in lower dimensions, where the bosons condense in a subspace of Hilbert space instead of a unique ground state, as well as condensation at fixed volume or fixed pressure. We show that Bose-Einstein condensation can lead to sub-shot-noise sensitivity for the measurement of the chemical potential. We also examine the influence of interactions on the sensitivity in three different models and show that mean-field and contact interactions deteriorate the sensitivity but only slightly for experimentally accessible weak interactions.

We observed two-photon phase superresolution in an unbalanced Michelson interferometer with classical Gaussian laser pulses. Our work is a time-reversed version of a two-photon interference experiment using an unbalanced Michelson interferometer. A measured interferogram exhibits two-photon phase superresolution with a high visibility of $97.9\%\pm 0.4\%$. Its coherence length is about 22 times longer than that of the input laser pulses. It is a classical analog to the large difference between the one- and two-photon coherence lengths of entangled photon pairs.

We have studied the effect of the spin-orbit interaction on generation and conversion of optical vortices in multihelicoidal fibers, that is, the fibers possessing a multihelical refractive index profile. On the basis of a fully analytical approach we have obtained the spectra of coupled modes and their structure. Specifically, we have established selection rules, under which the spin-orbit interaction mediates the conversion of optical vortices into vortices with the topological charge changed by $\pm \left(\ell \pm 2\right)$, $\ell$ being the number of helical branches in refractive index distribution. Also, we have shown that the spin-orbit interaction can lead to generation of radially and azimuthally polarized TE and TM modes from optical vortices. We have also demonstrated that if such generation is mediated by a scalar-type perturbation of the fiber's form, it is possible only for weakly deformed fibers. For strongly deformed fibers such perturbation can result only in generation of vortices with zero total angular momentum. Additionally, we have studied the possibility of polarization control over the orbital angular momentum of the generated state in such a system.

We study the problem of the $D$-dimensional $\delta$ potential, in nonrelativistic quantum mechanics, with modified Heisenberg algebra implying the existence of a minimal length. We show that the deformation parameter $\beta$ included initially in the formalism represents a natural cutoff so that the energy bound state is computed without imposing any extra condition.

Using photoelectron angular streaking by strong circularly polarized laser pulses, we measure angular-dependent tunneling rates from the inner orbitals of O${}_2$ in the molecular frame, which correlate with the strong-field molecular dissociative ionization process. We show that the electronic density of molecular inner orbitals can be visualized by angular tunneling rates in the molecular frame. We demonstrate the orbital-by-orbital characterization of tunneling ionization from randomly oriented molecules. Compared with the single-active-electron approximation theories, i.e., the molecular strong-field approximation and the molecular Ammosov-Delone-Krainov model, the experiment shows that the tunneling from the excited states and the state coupling might play an important role in strong-field molecular tunneling ionization. Our results suggest major advances in quantum theory needed for molecular inner orbital tunneling and open intriguing perspectives to probe quantum dynamics related with molecular core electrons.

We propose a feasible experiment in the context of cavity QED as follows: The initial state is a maximally entangled two cavity mode ($M_A$, $M_B$). Next a sequence of atoms are sent, one at a time, and interact with mode $M_B$. We show that the which-way information is initially stored only in $M_B$ is now distributed among the parties of the global system. The results realize known complementarity relations derived in the context of arbitrary qubits. We show that this dynamics may lead to a quantum eraser phenomenon provided that measurements of the probe atoms are performed in a basis which maximizes the visibility.

A realistic quantum-key-distribution protocol necessarily runs with finite resources. Usually, security proofs for existing quantum key distribution are asymptotic in the sense that certain parameters are exceedingly large compared to practical realistic values. In this paper, we derive bounds on the secret key rates for the Bennett 1992 protocol, which includes a preprocessing step. The derivation for a finite-size key is expressed as an optimization problem by using results from the uncertainty relations and the smooth Rényi entropies.