This study focuses on theoretical and numerical investigations of the magnetochiral (MCh) effect in the optical region. Electrodynamics in a medium with broken time and space inversions is described by two orthogonal coupled oscillators, in what is known as the Born-Kuhn model, subject to an external static magnetic field. Constitutive equations and the refractive index of the medium are theoretically derived. The results show that the MCh effect is induced even in the absence of an intrinsic interaction between the magneto-optical effect and the optical activity. The study also numerically investigates the electromagnetic response in a metamaterial with magnetism and chirality in the deep ultraviolet region. The results agree well with the main results of our theory. This paper paves the way to realizing MCh metamaterials in the optical region.

We study the structure of a Bose-condensed gas after quenching interactions to unitarity. Using the method of cumulants, we decompose the evolving gas in terms of clusters. Within the quantum depletion we observe the emergence of two-body clusters bound purely by many-body effects, scaling continuously with the atomic density. As the unitary Bose gas forms, three-body Efimov clusters are first localized and then sequentially absorbed into the embedded atom-molecule scattering continuum of the surrounding depletion. These results highlight the interplay of quantum depletion and evolving scaling laws in the formation of the unitary Bose gas.

We propose a learning method for estimating unknown pure quantum states. The basic idea of our method is to learn a unitary operation $\widehat{U}$ that transforms a given unknown state $|{\psi }_{\tau }\rangle$ to a known fiducial state $|f\rangle$. Then, after completion of the learning process, we can estimate and reproduce $|{\psi }_{\tau }\rangle$ based on the learned $\widehat{U}$ and $|f\rangle$. To realize this idea, we cast a random-based learning algorithm, called “single-shot measurement learning,” in which the learning rule is based on an intuitive and reasonable criterion: the greater the number of success (or failure), the less (or more) changes are imposed. Remarkably, the learning process occurs by means of a single-shot measurement outcome. We demonstrate that our method works effectively, i.e., the learning is completed with a finite number, say $N$, of unknown-state copies. Most surprisingly, our method allows the maximum statistical accuracy to be achieved for large $N$, namely $\simeq O\left(N^{-1}\right)$ scales of average infidelity. It highlights a nontrivial message, that is, a random-based strategy can potentially be as accurate as other standard statistical approaches.

A theoretical model for forbidden ortho-para absorption in molecules having weak intramolecular mixing of spin isomers is developed. The model is based on the quantum kinetic equation for the density matrix and uses the particular case of ${}^{13}\mathrm{CH}_3\mathrm{F}$ nuclear-spin isomers for numerical calculations. Forbidden ortho-para absorption appears to be very small, making its detection difficult in a standard approach. Two alternative methods for detection of forbidden ortho-para absorption are proposed. The methods use microwave enrichment of spin isomers and microwave speed up of the isomer conversion.

We discuss the detection of an anisotropic particle trapped by an elliptically polarized focused Gaussian laser beam. We obtain the full rotational and translational dynamics, as well as the measured photocurrent in a general-dyne detection. As an example, we discuss a toy model of homodyne detection, which captures the main features typically found in experimental setups.

A topological measure characterizing symmetry-protected topological phases in one-dimensional open fermionic systems is proposed. It is built upon the kinematic approach to the geometric phase of mixed states and facilitates the extension of the notion of topological phases from zero-temperature to nonzero-temperature cases. In contrast to a previous finding that topological properties may not survive above a certain critical temperature, we find that topological properties of open systems, in the sense of the measure suggested here, can persist at any finite temperature and disappear only in the mathematical limit of infinite temperature. Our result is illustrated with two paradigmatic models of topological matter. The bulk topology at nonzero temperatures manifested as robust mixed edge state populations is examined via two figures of merit.

We expand the class of holographic quantum error-correcting codes by developing the notion of block perfect tensors, a wider class that includes previously defined perfect tensors. The relaxation of this constraint opens up a range of other holographic codes. We demonstrate this by introducing the self-dual Calderbank-Shor-Steane (CSS) heptagon holographic code, based on the 7-qubit Steane code. Finally, we show promising thresholds for the erasure channel by applying a straightforward, optimal erasure decoder to the heptagon code and benchmark it against existing holographic codes.

The quantum variance of an observable is a fundamental quantity in quantum mechanics and provides additional information other than the average itself. By examining the relation between the particle-current variance ${\left(\delta J\right)}^2$ and the average current $J$ in both closed and open interacting fermionic systems, we show the emergence of a multivalued parametric curve between $\delta J$ and $J$ due to interactions. As a closed system we consider the persistent current in a benzenelike lattice enclosing an effective magnetic flux and solve it by exact diagonalization. For the open system, the steady-state current flowing through a few lattice sites coupled to two particle reservoirs is investigated using a Lindblad equation. In both cases, interactions open a loop and change the topology of the corresponding $\delta J\text{−}J$ curve, showing that this effect is model independent. We finally discuss how the predicted phenomenon can be observed in ultracold atoms, thus offering an alternative way of probing the dynamics of many-body systems.

Motivated by a recent experiment in an antiferromagnetic spin-1 Bose-Einstein condensate (BEC) of ${}^{23}\mathrm{Na}$ atoms, we study the energetic stability of a singly quantized vortex injected into the center of a quasi-two-dimensional gas with zero total spin against dissociation into a pair of half-quantum vortices, by using a variational ansatz. We find that the critical dissociation point of this confinement-deconfinement-type transition can be expressed in terms of the ratio of density-density ($c_0$) and spin-spin ($c_2$) coupling constants. The transition of bound to unbound vortices, in particular, sensitively depends on (1) the ratio of system size ($R$) to density healing length (${\xi }_d$), and (2) the trap potential. Specifically, the critical ratio ${(c_2/c_0)}_{\mathrm{cr}}$ increases when $R/{\xi }_d$ decreases and is relatively larger in a harmonic trap than in a box trap. Dissociation is energetically generally favored for $c_2/c_0<{(c_2/c_0)}_{\mathrm{cr}}$, which as a corollary implies that vortex dissociation is observed as well for negative $c_2<0$, e.g., in a rubidium spin-1 BEC, whereas in a sodium spin-1 BEC ($c_2>0$) it is energetically blocked above the critical ratio ${(c_2/c_0)}_{\mathrm{cr}}$. Tuning the coupling ratio $c_2/c_0$ by using microwave control techniques, the dependence of the deconfinement transition on coupling parameters, density, and system size we predict can be verified in experiments with ultracold spinor gases.

We explore the optomechanically induced transparency (OMIT) of a compound optomechanical system, which contains two cavities and a membrane. Due to the linear and quadratic coupling between the membrane and the cavity, i.e., ${\widehat{a}}_1^{†}{\widehat{a}}_1\widehat{q}$ and ${\widehat{a}}_1^{†}{\widehat{a}}_1{\widehat{q}}^2$, OMIT can be observed near $\delta ={\omega }_m$ and $\delta =2{\omega }_m$ simultaneously. The transmission rate of the probe field near $\delta =2{\omega }_m$ has the same order of magnitude with the transmission rate near $\delta ={\omega }_m$. This is in contrast to the second-order sideband OMIT effect which is caused by the intrinsic nonlinear optomechanical coupling. We also find that the positions of the two transmission windows depend on the power of the control field. By modulating the equilibrium position of the membrane, the transmission rate near $\delta ={\omega }_m$ can be controlled. The group delay of the transmitted light near $\delta ={\omega }_m$ is more sensitive to the equilibrium position of the membrane than the transmitted light near $\delta =2{\omega }_m$. So we can separate the two transmitted lights by modulating the equilibrium position of the membrane. Our investigation provides a method to steer the performance of OMIT devices.

We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurements subject to verifiable physical constraints and with respect to classical side information. Examples include randomness from single-photon measurements and device-independent randomness from Bell tests. Advantages of probability estimation include unproblematic early stopping when goals are achieved, optimal randomness rates, applicability to Bell tests with small violations, and unsurpassed finite-data efficiency. We greatly reduce latencies for producing random bits and formulate an associated rate-tradeoff problem of independent interest. We also show that the latency is determined by an information-theoretic measure of nonlocality rather than the Bell violation.

Cold atoms tailored by an optical lattice have become a fascinating arena for simulating quantum physics. In this area, one important and challenging problem is creating effective spin-orbit coupling (SOC), especially for fashioning a cold atomic gas into a topological phase, for which prevailing approaches mainly rely on the Raman coupling between the atomic internal states and a laser field. Herein, a strategy for realizing effective SOC is proposed by exploiting the geometric effects in the effective-mass theory, without resorting to internal atomic states. It is shown that the geometry of Bloch states can have nontrivial effects on the wave-mechanical states under external fields, leading to effective SOC and an effective Darwin term, which have been neglected in the standard effective-mass approximation. It is demonstrated that these relativisticlike effects can be employed to introduce effective SOC in a two-dimensional optical superlattice, and induce a nontrivial topological phase.

In a recent Letter by Budroni and Emary [Phys. Rev. Lett. 113, 050401 (2014)], it is shown that the quantum violation of a three-time Leggett-Garg inequality for a dichotomic qutrit system can exceed the Lüders bound. This is obtained by using a degeneracy-breaking projective measurement rule which the authors termed the “von Neumann rule.” Such violation can even approach the algebraic maximum in the asymptotic limit of system size. In this paper, we first examine the reason behind such violation of the Lüders bound in quantum mechanics and its conceptual relevance in the Leggett-Garg scenario. Further, we demonstrate the violation of the Lüders bound of the simplest noncontextual inequality involving three commuting observables. The implication of such violations of the Lüders bound of Leggett-Garg inequalities and noncontextual inequalities is discussed.

This paper proposes a revised definition for the entanglement cost of a quantum channel $\mathcal{N}$. In particular, it is defined here to be the smallest rate at which entanglement is required, in addition to free classical communication, in order to simulate $n$ calls to $\mathcal{N}$, such that the most general discriminator cannot distinguish the $n$ calls to $\mathcal{N}$ from the simulation. The most general discriminator is one who tests the channels in a sequential manner, one after the other, and this discriminator is known as a quantum tester [Chiribella et al., Phys. Rev. Lett. 101, 060401 (2008)] or one who is implementing a quantum costrategy [Gutoski and Watrous, in Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing STOC '07 (ACM Press, New York, 2007), pp. 565–574]. As such, the proposed revised definition of entanglement cost of a quantum channel leads to a rate that cannot be smaller than the previous notion of a channel's entanglement cost [Berta et al., IEEE Trans. Inf. Theory 59, 6779 (2013)], in which the discriminator is limited to distinguishing parallel uses of the channel from the simulation. Under this revised notion, I prove that the entanglement cost of certain teleportation-simulable channels is equal to the entanglement cost of their underlying resource states. Then I find single-letter formulas for the entanglement cost of some fundamental channel models, including dephasing, erasure, three-dimensional Werner-Holevo channels, and epolarizing channels (complements of depolarizing channels), as well as single-mode pure-loss and pure-amplifier bosonic Gaussian channels. These examples demonstrate that the resource theory of entanglement for quantum channels is not reversible. Finally, I discuss how to generalize the basic notions to arbitrary resource theories.

We propose a method to produce fast transitionless dynamics for finite-dimensional quantum systems without requiring additional Hamiltonian components not included in the initial control setup, remaining close to the true adiabatic path at all times. The strategy is based on the introduction of an effective counterdiabatic scheme: a correcting Hamiltonian is constructed which approximatively cancels nonadiabatic effects, inducing an evolution tracking the adiabatic states closely. This can be absorbed into the initial Hamiltonian by adding a fast oscillation in the control parameters. We show that a consistent speedup can be achieved without requiring strong control Hamiltonians, using it both as a stand-alone shortcut to adiabaticity and as a weak correcting field. A number of examples are treated, dealing with quantum state transfer in avoided-crossing problems and entanglement creation.

The features of the self-action of a wave field in a small-sized optical system consisting of $2N$ identical light guides, which are disposed equidistantly along a ring, and an isolated fiber in the center are studied analytically and numerically. Stable exact solutions are found for intense wave beams in such a system, allowing long-distance coherent transport of radiation in a set of optical fibers. The total beam power in this case can exceed several times the critical power of self-focusing in the continuous medium. This is clearly manifested for the out-of-phase spatial distribution of $u_n={(-1)}^{n}f$, which is stable at arbitrary powers. Direct numerical simulation of the nonlinear unidirectional wave propagation equation confirms the stability of found wave field distributions.

We investigate theoretically the model of a cavity-quantum-electrodynamics (QED) system that consists of two two-level atoms coupled to a single-mode cavity in the weak coupling regime, where the system is driven by quantum light. The dynamics behavior of the entire system is tackled in the framework of a cascaded quantum system. We find that the two-photon blockade with two-photon bunching and three-photon antibunching can be obtained even when the strong system dissipation is included. This result shows that our work has potential for realizing entangled photon pairs in a weakly coupled cavity. Moreover, we also analyze the photon statistics of the system in the case of out-of-resonance coupling between cavity and two nonidentical atoms. Here, an unconventional photon blockade effect with suppression of two-photon correlation and enhancement of three-photon correlation can be realized, which shows many quantum statistical characteristics of a cavity QED system in weak coupling.

Quantum evaporation may occur in a variety of systems such as superfluids, Bose-Einstein condensates, and gravitational black holes (Hawking radiation). However, to date all predictions are based on semiclassical models, e.g., the Einstein equations and classical space-time metric for a black hole and only the fluctuations are quantized. Here we use a fully quantized dynamical equation, the quantum nonlinear Schrödinger equation, to study the evolution of quantum solitons. As a result of quantum fluctuations in the center-of-mass position, the expectation value of the quantum soliton width increases and concomitantly evaporates through the emission of frequency-entangled photon pairs. The frequency of this emission decreases as the soliton evaporates due to the soliton spreading. In the final phase, the soliton mean field collapses irreversibly into a state with zero mean amplitude. These results may provide insight to quantum evaporation in other systems where a full quantum description is still to be developed and highlights that even classically stable systems may also be subject to quantum evaporation.