Multiphoton entangled states are a crucial resource for many applications in quantum information science. Semiconductor quantum dots offer a promising route to generate such states by mediating photon-photon correlations via a confined electron spin, but dephasing caused by the host nuclear spin environment typically limits coherence (and hence entanglement) between photons to the spin $T_2^{*}$ time of a few nanoseconds. We propose a protocol for the deterministic generation of multiphoton entangled states that is inherently robust against the dominating slow nuclear spin environment fluctuations, meaning that coherence and entanglement is instead limited only by the much longer spin $T_2$ time of microseconds. Unlike previous protocols, the present scheme allows for the generation of very low error probability polarization encoded three-photon GHZ states and larger entangled states, without the need for spin echo or nuclear spin calming techniques.

We study the energy deposition in a one-dimensional interacting quantum system with a pointlike potential modulated in amplitude. The pointlike potential at position $x=0$ has a constant part and a small oscillation in time with a frequency $\omega$. We use bosonization, renormalization group, and linear response theory to calculate the corresponding energy deposition. It exhibits a power law behavior as a function of the frequency that reflects the Tomonaga-Luttinger liquid (TLL) nature of the system. Depending on the interactions in the system, characterized by the TLL parameter $K$ of the system, a crossover between weak and strong coupling for the backscattering due to the potential is possible. We compute the frequency scale ${\omega }_{*}$, at which such crossover exists. We find that the energy deposition due to the backscattering shows different exponents for $K>1$ and $K<1$. We discuss possible experimental consequences, in the context of cold atomic gases, of our theoretical results.

We have recently shown that the electromagnetic pulse in a medium is made of mass-polariton (MP) quasiparticles, which are quantized coupled states of the field and an atomic mass density wave (MDW) [M. Partanen et al., Phys. Rev. A 95, 063850 (2017)]. In this work, we generalize the MP theory of light for dispersive media assuming that absorption and scattering losses are very small. Following our previous work, we present two different approaches to the coupled state of light: (1) the MP quasiparticle theory, which is derived by only using the fundamental conservation laws and the Lorentz transformation; (2) the classical optoelastic continuum dynamics (OCD), which is a generalization of the electrodynamics of continuous media to include the dynamics of the medium under the influence of optical forces. We show that the total momentum and the transferred mass of the light pulse can be determined in a straightforward way if we know the field energy of the pulse and the dispersion relation of the medium. In analogy to the nondispersive case, we also find unambiguous correspondence between the MP and OCD theories. For the coupled MP state of a single photon and the medium, we obtain the total MP momentum $p_{\mathrm{MP}}=n_{\mathrm{p}}\hslash \omega /c$, where $n_{\mathrm{p}}$ is the phase refractive index. The field's share of the MP momentum is equal to $p_{\mathrm{field}}=\hslash \omega /\left(n_{\mathrm{g}}c\right)$, where $n_{\mathrm{g}}$ is the group refractive index and the share of the MDW is equal to $p_{\mathrm{MDW}}=p_{\mathrm{MP}}-p_{\mathrm{field}}$. Thus, as in a nondispersive medium, the total momentum of the MP is equal to the Minkowski momentum and the field's share of the momentum is equal to the Abraham momentum. We also show that the correspondence between the MP and OCD models and the conservation of momentum at interfaces gives an unambiguous formula for the optical force. The dynamics of the light pulse and the related MDW lead to nonequilibrium of the medium and to relaxation of the atomic density by sound waves in the same way as for nondispersive media. We also carry out simulations for optimal measurements of atomic displacements related to the MDW in silicon. In the simulations, we consider different waveguide cross sections and optical pulse widths and account for the breakdown threshold irradiance of materials. We also compare the MP theory to previous theories of the momentum of light in a dispersive medium. We show that our generalized MP theory resolves all the problems related to the Abraham-Minkowski dilemma in a dispersive medium.

The effects of group- and phase-velocity mismatch are well known in optical harmonic generation, but the nondegenerate cases remain unexplored. In this work we develop an analytic model which predicts velocity mismatch effects in nondegenerate triple sum-frequency mixing, TSF. We verify this model experimentally using two tunable, ultrafast, short-wave IR lasers to demonstrate spectral fringes in the TSF output from a 500-$\mu \mathrm{m}$-thick sapphire plate. We find the spectral dependence of the TSF depends strongly on both the phase-velocity and the group-velocity differences between the input and output fields. We define practical strategies for mitigating the impact of velocity mismatches.

A growing number of experimental setups in cavity optomechanics exploit periodically driven fields. However, such setups are not amenable to analysis by using simple, yet powerful, closed-form expressions of linearized optomechanics, which have provided so much of our present understanding of experimental optomechanics. In the present paper, we formulate a method to calculate quantum noise spectra in modulated optomechanical systems, which we analyze, compare, and discuss with two other recently proposed solutions: we term these (i) frequency-shifted operators, (ii) Floquet [Phys. Rev. A 94, 023803 (2016)], and (iii) iterative analysis [New J. Phys. 18, 113021 (2016)]. We prove that (i) and (ii) yield equivalent noise spectra and find that (iii) is an analytical approximation to (i) for weak modulations. We calculate the noise spectra of a doubly modulated system describing experiments of levitated particles in hybrid electro-optical traps. We show excellent agreement with Langevin stochastic simulations in the thermal regime and predict squeezing in the quantum regime. Finally, we reveal how otherwise-inaccessible spectral components of a modulated system can be measured in heterodyne detection through an appropriate choice of modulation frequencies.

We provide an exact solution of the scattering problem for the potentials of the form $v(x,y)={\chi }_a\left(x\right)[v_0\left(x\right)+v_1\left(x\right)e^{i\alpha y}]$, where ${\chi }_a\left(x\right):=1$ for $x\in [0,a]$, ${\chi }_a\left(x\right):=0$ for $x\notin [0,a]$, $v_j\left(x\right)$ are real or complex-valued functions, ${\chi }_a\left(x\right)v_0\left(x\right)$ is an exactly solvable scattering potential in one dimension, and $\alpha$ is a positive real parameter. If $\alpha$ exceeds the wave number $k$ of the incident wave, the scattered wave does not depend on the choice of $v_1\left(x\right)$. In particular, $v(x,y)$ is invisible if $v_0\left(x\right)=0$ and $k<\alpha$. For $k>\alpha$ and $v_1\left(x\right)\ne 0$, the scattered wave consists of a finite number of coherent plane-wave pairs ${\psi }_n^{\pm }$ with wave vector: ${\mathbf{k}}_n=(\pm \sqrt{k^2-{\left[n\alpha \right]}^2},n\alpha )$, where $n=0,1,2,...<k/\alpha$. This generalizes to the scattering of wave packets and suggests means for generating quantum states with a quantized component of momentum and pairs of states with an entangled momentum. We examine a realization of these potentials in terms of certain optical slabs. If $k=N\alpha$ for some positive integer $N$, ${\psi }_N^{\pm }$ coalesce and their amplitude diverge. If $k$ exceeds $N\alpha$ slightly, ${\psi }_N^{\pm }$ have a much larger amplitude than ${\psi }_n^{\pm }$ with $n<N$. This marks a resonance effect that arises for the scattered waves whose wave vector makes a small angle with the faces of the slab.

We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities is their nonlinearity; this has nontrivial consequences for the derivation of their local bound, which is not reached by deterministic local correlations. For our simplest inequality, we derive analytically tight bounds for both local and quantum correlations. An interesting application of covariance Bell inequalities is that they can act as “shared randomness witnesses”: specifically, the value of the Bell expression gives device-independent lower bounds on both the dimension and the entropy of the shared random variable in a local model.

Interaction-free measurement is a quantum process where, in the ideal situation, an object can be detected as if no interaction took place with the probing photon. Here we show that the problem of interaction-free measurement can be regarded as a problem of quantum-channel discrimination. In particular, we look for the optimal photonic states that can minimize the detection error and the photon loss in detecting the presence or absence of the object, which is taken to be semitransparent, and the number of the interrogation cycle is assumed to be finite. Furthermore, we also investigated the possibility of minimizing the detection error through the use of entangled photons, which is essentially a setting of quantum illumination. However, our results indicate that entanglement does not exhibit a clear advantage; the same performance can be achieved with unentangled photonic states.

The promise of quantum neural nets, which utilize quantum effects to model complex data sets, has made their development an aspirational goal for quantum machine learning and quantum computing in general. Here we provide methods of training quantum Boltzmann machines. Our work generalizes existing methods and provides additional approaches for training quantum neural networks that compare favorably to existing methods. We further demonstrate that quantum Boltzmann machines enable a form of partial quantum state tomography that further provides a generative model for the input quantum state. Classical Boltzmann machines are incapable of this. This verifies the long-conjectured connection between tomography and quantum machine learning. Finally, we prove that classical computers cannot simulate our training process in general unless $\text{BQP}=\text{BPP}$, provide lower bounds on the complexity of the training procedures and numerically investigate training for small nonstoquastic Hamiltonians.

We present a proof-of-principle demonstration of a method to characterize any pure spatial qudit of arbitrary dimension $d$, which is based on the classic phase-shift interferometry technique. In the proposed scheme a total of only $4d$ measurement outcomes are needed, implying a significant reduction with respect to the standard schemes for quantum-state tomography which require on the order of $d^2$. By using this technique, we have experimentally reconstructed a large number of states ranging from $d=2$ up to 14 with mean fidelity values higher than 0.97. For that purpose the qudits were codified in the discretized transverse-momentum position of single photons, once they are sent through an aperture with $d$ slits. We provide an experimental implementation of the method based in a Mach-Zehnder interferometer, which allows one to reduce the number of measurement settings to four since the $d$ slits can be measured simultaneously. Furthermore, it can be adapted to consider the reconstruction of the unknown state from the outcome frequencies of $4d-3$ fixed projectors independently of the encoding or the nature of the quantum system, allowing one to implement the reconstruction method in a general experiment.

We present a theoretical study of the finite-temperature Kosterlitz-Thouless (KT) and vortex-antivortex lattice (VAL) melting transitions in two-dimensional Fermi gases with $p$- or $d$-wave pairing. For both pairings, when the interaction is tuned from weak to strong attractions, we observe a quantum phase transition from the Bardeen-Cooper-Schrieffer (BCS) superfluidity to the Bose-Einstein condensation (BEC) of difermions. The KT and VAL transition temperatures increase during this BCS-BEC transition and approach constant values in the deep BEC region. The BCS-BEC transition is characterized by the nonanalyticities of the chemical potential, the superfluid order parameter, and the sound velocities as functions of the interaction strength at both zero and finite temperatures; however, the temperature effect tends to weaken the nonanalyticities compared to the zero-temperature case. The effect of mismatched Fermi surfaces on the $d$-wave pairing is also studied.

When dressed particles (polarons) exchange quantum phonons, the resulting interactions are generally attractive. If the particles have hard-core statistics and the coupling to phonons is through the kinetic energy terms, phonon-mediated interactions are repulsive. Here, we show that such repulsive phonon-mediated interactions bind dressed particles into bipolarons with unique properties. These bipolaron states appear in the gap between phonon excitations, above the two-polaron continuum. While thermodynamically unstable, the bipolaron is protected by energy and momentum conservation and represents a quasiparticle with a large dispersion and a negative effective mass near zero momentum. We discuss possible experimental implementation of the conditions for the formation of such repulsively bound bipolarons.

We report on heralded-single-photon superradiant beating in the spontaneous four-wave mixing process of Doppler-broadened ladder-type ${}^{87}\mathrm{Rb}$ atoms. When Doppler-broadened atoms contribute to two-photon coherence, the detection probability amplitudes of the heralded single photons are coherently superposed despite inhomogeneous broadened atomic media. Single-photon superradiant beating is observed, which constitutes evidence for the coherent superposition of two-photon amplitudes from different velocity classes in the Doppler-broadened atomic ensemble. We present a theoretical model in which the single-photon superradiant beating originates from the interference between wavelength-separated two-photon amplitudes via the reabsorption filtering effect.

We consider optical bound states in the continuum (BICs) in periodic arrays of dielectric rods. The full classification of BICs in the above system is provided, including the modes propagating along the axes of the rods and bidirectional BICs propagating both along the axes of the rods and the axis of periodicity. It is shown that the leaky zones supporting the BICs generally have elliptically polarized far-field radiation patterns, with the polarization ellipses collapsing on approach to the BICs in momentum space. That allowed us to apply the concept of polarization singularities and demonstrate that the BICs possess a topological charge defined as the winding number of the polarization direction [Phys. Rev. Lett. 113, 257401 (2014)]. It is found that the evolution of the BICs, including their creation and annihilation, under variation of geometric parameters is controlled by the topological charge. Three scenarios of such evolution for different leaky zones are described. Finally, it is shown that the topological properties of the BICs can be extracted from transmission spectra when the system is illuminated by a plane wave of circular polarization.

Since the enlightening proofs of quantum contextuality first established by Kochen and Specker, and also by Bell, various simplified proofs have been constructed to exclude the noncontextual hidden variable theory of our nature at the microscopic scale. The conflict between the noncontextual hidden variable theory and quantum mechanics is commonly revealed by Kochen-Specker sets of yes-no tests, represented by projectors (or rays), via either logical contradictions or noncontextuality inequalities in a state-(in)dependent manner. Here we propose a systematic and programmable construction of a state-independent proof from a given set of nonspecific rays in ${\mathbb{C}}^3$ according to their Gram matrix. This approach brings us a greater convenience in the experimental arrangements. Besides, our proofs in ${\mathbb{C}}^3$ can also be generalized to any higher-dimensional systems by a recursive method.

We study the behavior of non-Markovianity with respect to the localization of the initial environmental state. The “amount” of non-Markovianity is measured using divisibility and distinguishability as indicators, employing several schemes to construct the measures. The system used is a qubit coupled to an environment modeled by an Ising spin chain kicked by ultrashort pulses of a magnetic field. In the integrable regime, non-Markovianity and localization do not have a simple relation, but as the chaotic regime is approached, simple relations emerge, which we explore in detail. We also study the non-Markovianity measures in the space of the parameters of the spin coherent states and point out that the pattern that appears is robust under the choice of the interaction Hamiltonian but does not have a classical-like phase-space structure.