We investigate second-harmonic generation in III-V semiconductor wire waveguides aligned with a crystallographic axis. In this direction, because of the single nonzero tensor element coming from the zinc-blende symmetry of III-V semiconductors, only frequency conversion by mixing with the longitudinal components of the optical fields is allowed. We experimentally study the impact of the propagation direction on the conversion efficiency and confirm the role played by the longitudinal components through the excitation of an antisymmetric second-harmonic higher-order mode.

In this paper, we study the exact dynamics of general open systems interacting with their environments through particle exchanges. The paper includes two main results. First, by taking advantage of the propagating function in the coherent state representation, we obtain the exact solution of the reduced density matrix, which is expressed in terms of the nonequilibrium Green functions. Second, in the dynamical perspective, we provide a rigorous thermalization process of open quantum systems.

With the current interest in building quantum computers, there is a strong need for accurate and efficient characterization of the noise in quantum gate implementations. A key measure of the performance of a quantum gate is the minimum gate fidelity, i.e., the fidelity of the gate, minimized over all input states. Conventionally, the minimum fidelity is estimated by first accurately reconstructing the full gate process matrix using the experimental procedure of quantum process tomography (QPT). Then, a numerical minimization is carried out to find the minimum fidelity. QPT is, however, well known to be costly, and it might appear that we can do better if the goal is only to estimate one single number. In this work, we propose a hybrid numerical-experimental scheme that employs a numerical gradient-free minimization (GFM) and an experimental target-fidelity estimation procedure to directly estimate the minimum fidelity without reconstructing the process matrix. We compare this to an alternative scheme, referred to as QPT fidelity estimation, that does use QPT, but directly employs the minimum gate fidelity as the termination criterion. Both approaches can thus be considered as direct estimation schemes. General resource estimates suggest a significant resource savings for the GFM scheme over QPT fidelity estimation; numerical simulations for specific classes of noise, however, show that both schemes have similar performance, reminding us of the need for caution when using general bounds for specific examples. The GFM scheme, however, presents potential for future improvements in resource cost, with the development of even more efficient GFM algorithms.

A time crystal is defined as a phase of matter spontaneously exhibiting a periodicity in time. Previous studies focused on discrete quantum time crystals under periodic drive. Here, we propose a time crystal model based on a levitated charged nanoparticle in a static magnetic field without drive. Both the classical time crystal in thermal equilibrium and the quantum time crystal in the ground state can emerge in the spin rotational mode, under a strong magnetic field or large charge-to-mass ratio limit. Additionally, the time polycrystal is defined and naturally appears in this model. Our model paves a way for realizing time crystals in thermal equilibrium.

We develop an all-optical method to rapidly produce a large ${}^{85}\mathrm{Rb}$ Bose-Einstein condensate. ${}^{85}\mathrm{Rb}$ has a reputation as a difficult species to cool to quantum degeneracy due to its collisional properties. We solve these intrinsic difficulties by a combination of polarization gradient cooling in a 3D optical lattice and a compressible double-crossed dipole trap (DCDT). This lattice cooling circumvents the low rethermalization rate and loads more than ${10}^7$ atoms with a phase-space density larger than ${10}^{-3}$ into the enlarged DCDT. The subsequent compressions and evaporations in the size-adjustable DCDT can maximize the cooling efficiency while reducing unnecessary inelastic losses. We fix the bias magnetic field to 161 G where the $s$-wave scattering length is positive and large. The forced evaporations function well against inelastic collisions at an average density of $5\times {10}^{12}{\mathrm{cm}}^{-3}$. A nearly pure condensate of $2\times {10}^5$ atoms is produced in 3.2 s of evaporation time.

We study the spin squeezing in a spin-1/2 Bose-Einstein condensates (BEC) with Raman-induced spin-orbit coupling (SOC). Under the condition of two-photon resonance and weak Raman coupling strength, the system possesses two degenerate ground states, using which we construct an effective two-mode model. The Hamiltonian of the two-mode model takes the form of the one-axis-twisting Hamiltonian, which is known to generate spin squeezing. More importantly, we show that the SOC provides a convenient control knob to adjust the spin nonlinearity responsible for spin squeezing. Specifically, the spin nonlinearity strength can be tuned to be comparable to the two-body density-density interaction, and hence is much larger than the intrinsic spin-dependent interaction strength in conventional two-component BEC systems such as ${}^{87}\mathrm{Rb}$ and ${}^{23}\mathrm{Na}$ in the absence of the SOC. We confirm the spin squeezing by carrying out a fully beyond-mean-field numerical calculation using the truncated Wigner method. Additionally, the experimental implementation is also discussed.

We propose a mechanism to engineer a chiral spectral flow of interface states in a gapless semimetallic system. Although the topological indices of the bands (Chern numbers) remain ill-defined, owing to the existence of bulk band touching points, this spectral flow has a topological origin that makes it robust even when it coexists with the bulk bands. These interface states between two gapless Dirac semimetals generalize the usual ones appearing between two topologically distinct insulators. This phenomenon is illustrated with an adiabatically modulated photonic quantum walk.

In this paper we consider the Liouville equation that describes the quantum nonunitary dynamics of quantum states in optical fiber. We consider a particular case of thermalization aiming to applications related to various quantum information protocols; however, the model can be generalized in various ways taking into account more features (external pump, nonlinear interactions, continuous spectra, free space propagation, etc.). In order to obtain the appropriate evolution models for states in the channel we use the $\text{su}(1,1)$ algebra formalism in the Liouville representation. The developed model is applied in cases of two different initial states as an example. The first is single- and multifrequency-mode (e.g., wavelength-division-multiplexed) weak coherent states in quantum notation as a rather simple but useful example. This particular example is of interest since weak coherent states are a commonly used tool in various fields of optics, e.g., optical communication, quantum key distribution, etc. Results for coherent states are well agreed upon with classical theories; however, in order to highlight quantum features of developed theory we also consider the case of nonclassical light, in particular, Fock states. Considered implementation of the model takes into account dichroism, retardance, thermalization, dispersion, and decoherence in the polarization domain. We derive expressions of evolved states, mean photon number, and estimate the Stokes parameters as well as the degree of polarization. Considered examples explicitly demonstrate all the features and effects of the developed approach. The described approach allows one to connect the information properties of quantum channels with its physical ones. In order to illustrate this statement we consider BB84 quantum key distribution protocol and investigate the behavior of the quantum bit error rate affected by considered physical phenomena in an optical fiber.

We show that the effects of decoherence on quantum steering ellipsoids can be controlled by a specific reservoir manipulating, in both Markovian and non-Markovian realms. Therefore, the so-called maximal steered coherence could be protected through reservoir engineering implemented by coupling auxiliary qubits to the reservoir.

The WKB analysis for higher order differential equations had not been developed until recent progress of the so-called exact WKB method, so it was difficult to find WKB solutions for multistate nonadiabatic models in general, whereas enormous efforts were made especially for the study of generalized Landau-Zener models. Under such circumstances Aoki-Kawai-Takei provided a closed expression for the $S$ matrix of a time-dependent multistate nonadiabatic system, in which diabatic potential curves are given as polynomial functions of time and they all intersect with each other. Their result is completely explicit, and the model covers much wider classes of systems than multistate nonadiabatic models studied so far. Here we numerically show how their exact WKB formula works as long as crossing points of diabatic potential curves are well separated. The model studied includes the cases where diabatic potential functions are nonlinear, not like generalized Landau-Zener models. We also discuss the situations where virtual turning points and new Stokes curves, new components in the Stokes geometry appearing only for higher order differential equations, come into play. In particular, we examine how the presence of new Stokes curves affects final transition probabilities using a couple of concrete examples.

Leggett and Garg defined macrorealism by positing that a macroscopic system will exist in a well-defined state at all times, and that this state can be measured without disturbing it. They also formulated a class of inequalities which hold under macrorealism but can be violated by quantum mechanics. The degree to which quantum systems can violate these inequalities is restricted by the temporal Tsirelson bounds. Recently variants of Leggett-Garg inequalities which can be violated to the algebraic maximum 3 for a sufficient large number of measurement times have been proposed. In this work we report an experimental test of quantum violation of the variants of Leggett-Garg inequalities beyond the temporal Tsirelson bounds, up to $2.248\pm 0.039$ in five-time measurement scenarios for a photonic qubit. Our results clearly show the advantages of the modified measurement scenarios.

To prove the security of quantum key distribution (QKD) protocols, several assumptions have to be imposed on users' devices. From an experimental point of view, it is preferable that such theoretical requirements are feasible and the number of them is small. In this paper, we provide a security proof of a QKD protocol where the usage of any light source is allowed as long as it emits two independent and identically distributed (i.i.d.) states. Our QKD protocol is composed of two parts: the first part is characterization of the photon-number statistics of the emitted signals up to three-photons based on the method [M. Kumazawa, T. Sasaki, and M. Koashi, Opt. Express 27, 5297 (2019)], followed by running our differential-phase-shift protocol [A. Mizutani, T. Sasaki, Y. Takeuchi, K. Tamaki, and M. Koashi, npj Quantum Inf. 5, 87 (2019)]. It is remarkable that as long as the light source emits two i.i.d. states, even if we have no prior knowledge of the light source, we can securely employ it in the QKD protocol. As this result substantially simplifies the requirements on light sources, it constitutes a significant contribution to realizing truly secure quantum communication.

We study the properties of a $2+1$-dimensional sonic black hole (SBH) that can be realized in a quasi-two-dimensional two-component spin-orbit-coupled Bose-Einstein condensate (BEC). The corresponding equation for phase fluctuations in the total density mode that describes phonon field in the hydrodynamic approximation is described by a scalar field equation in $2+1$ dimension whose space-time metric is significantly different from that of the SBH realized from a single component BEC that was studied experimentally and, theoretically, meticulously in literature. Given the breakdown of the irrotationality constraint of the velocity field in such spin-orbit-coupled BEC, we study in detail how the time evolution of such a condensate impacts the various properties of the resulting SBH. By time evolving the condensate in a suitably created laser-induced potential, we show that such a sonic black hole is formed in an annular region bounded by an inner and outer event horizon as well as elliptical ergosurfaces. We observe amplifying density modulation due to the formation of such sonic horizons and show how they change the nature of analog Hawking radiation emitted from such a sonic black hole by evaluating the density-density correlation at different times, using the truncated Wigner approximation (TWA) for different values of spin-orbit coupling parameters. We finally investigate the thermal nature of such analog Hawking radiation.

Spontaneous symmetry breaking and formation of self-organized structures in nonlinear systems are intriguing and important phenomena in nature. Advancing such research to new nonlinear optical regimes is of much interest for both fundamental physics and practical applications. Here we propose a scheme to realize optical pattern formation in a cold Rydberg atomic gas via electromagnetically induced transparency. We show that, by coupling two Rydberg states with a microwave field (microwave dressing), the nonlocal Kerr nonlinearity of the Rydberg gas can be enhanced significantly and may be tuned actively. Based on such nonlocal Kerr nonlinearity, we demonstrate that a plane-wave state of a probe laser field can undergo a modulation instability (MI) and hence spontaneous symmetry breaking, which may result in the emergence of various self-organized optical patterns. Especially, we find that a hexagonal lattice pattern (which is the only optical pattern when the microwave dressing is absent) may develop into several types of square lattice ones when the microwave dressing is applied; moreover, as an outcome of the MI the formation of nonlocal optical solitons is also possible in the system. The optical patterns and nonlocal optical solitons found here can be flexibly manipulated by adjusting the effective probe-field intensity, nonlocality degree of the Kerr nonlinearity, and strength of the microwave field. Our paper opens a route for versatile controls of self-organizations and structural phase transitions of laser light, which may have potential applications in optical information processing and transmission.

We formulate an algorithm to lower bound the fidelity between quantum many-body states only from partial information, such as the one accessible by few-body observables. Our method is especially tailored to permutationally invariant states, but it gives nontrivial results in all situations where this symmetry is even partial. This property makes it particularly useful for experiments with atomic ensembles, where relevant many-body states can be certified from collective measurements. As an example, we show that a ${\xi }^2\approx -6\text{dB}$ spin squeezed state of $N=100$ particles can be certified with a fidelity up to $F=0.999$, only from the measurement of its polarization and of its squeezed quadrature. Moreover, we show how to quantitatively account for both measurement noise and partial symmetry in the states, which makes our method useful in realistic experimental situations.

We present quantum algorithms for the estimation of $n$-time correlation functions, the local and nonlocal density of states, and dynamical linear response functions. These algorithms are all based on block encodings—a versatile technique for the manipulation of arbitrary nonunitary matrices on a quantum computer. We describe how to “sketch” these quantities via the kernel polynomial method which is a standard strategy in numerical condensed-matter physics. These algorithms use amplitude estimation to obtain a quadratic speedup in the accuracy over previous results, can capture any observables and Hamiltonians presented as linear combinations of Pauli matrices, and are modular enough to leverage future advances in Hamiltonian simulation and state preparation.

The spectral-density operator $\widehat{\rho }\left(\omega \right)=\delta (\omega -\widehat{H})$ plays a central role in linear response theory as its expectation value, the dynamical response function, can be used to compute scattering cross sections. In this work, we describe a near optimal quantum algorithm providing an approximation to the spectral density with energy resolution $\mathrm{\Delta }$ and error $\epsilon$ using $O\left(\sqrt{{log}_2\left(1/\epsilon \right)\left[{log}_2\left(1/\mathrm{\Delta }\right)+{log}_2\left(1/\epsilon \right)\right]}/\mathrm{\Delta }\right)$ operations. This is achieved without using expensive approximations to the time-evolution operator, but instead exploiting qubitization to implement an approximate Gaussian integral transform of the spectral density. We also describe appropriate error metrics to assess the quality of the spectral function approximations more generally.

The hyperfine structure (HFS) of atomic energy levels arises due to interactions of atomic electrons with a hierarchy of nuclear multipole moments, including magnetic dipole, electric quadrupole, and higher rank moments. Recently, a determination of the magnetic octupole moment of the ${}^{173}\mathrm{Yb}$ nucleus was reported from HFS measurements in neutral ${}^{173}\mathrm{Yb}$ [A. K. Singh et al., Phys. Rev. A 87, 012512 (2013)] and is four orders of magnitude larger than the nuclear theory prediction. Considering this substantial discrepancy between the spectroscopically extracted value and nuclear theory, here we propose to use an alternative system to resolve this tension—a singly charged ion of the same ${}^{173}\mathrm{Yb}$ isotope. Utilizing the substantial suite of tools developed around ${\mathrm{Yb}}^{+}$ for quantum information applications, we propose to extract nuclear octupole and hexadecapole moments from measuring hyperfine splittings in the extremely long-lived first excited state [$4f^{13}\left({}^{2}F^o\right)6s^2, J=7/2$] of ${}^{173}\mathrm{Yb}^{+}$. We present results of atomic structure calculations in support of the proposed measurements.

The van der Waals potential energy of a linear dipole array is calculated based on a formula using a determinant of a matrix determining the dipole interactions, which includes all orders of the coupling strength and can be applied to a system with an arbitrary number of dipoles. To consider the nonadditivity of the van der Waals interactions, the van der Waals potential energy is expressed as a series of ratios of the susceptibility of the dipole to a cubic root of the distance between the nearest-neighboring dipoles, up to the fourth order for different numbers of dipoles. We show that the contribution of the terms including nonadditive interactions between four dipoles increases with the total number of dipoles and exceeds that between two dipoles. Furthermore, the error in the series expansion is evaluated by comparing the exact potential energy, including all orders of the coupling strength for a small number of dipoles.