The low-density expansions for the energy, chemical potential, and condensate depletion of the homogeneous dilute dipolar Bose gas are obtained by regularizing the dipole-dipole interaction at long distances. It is shown that the leading term, proportional to the density, allows a simple physical interpretation and consistently describes the thermodynamic stability of the system. The long-range asymptotics are obtained analytically for the normal and anomalous one-particle correlation functions and the pair distribution function. We discuss the properties of the two-body scattering with zero relative momentum for the dipole-dipole interaction; in particular, we derive the asymptotics of the wave function and a correction to the scattering length for small values of the dipolar range. We show how the density expansions can be derived within the Bogoliubov model of weakly interacting particles without any divergence from the assumption of universality of the expansions at low densities.

Quenches are now routinely used in synthetic quantum systems to study a variety of fundamental effects, including ergodicity breaking, light-cone-like spreading of information, and dynamical phase transitions. It was shown recently that the dynamics of equal-time correlators may be related to ground-state phase transitions and some properties of the system excitations. Here, we show that the full low-lying excitation spectrum of a generic many-body quantum system can be extracted from the after-quench dynamics of equal-time correlators. We demonstrate it for a variety of one-dimensional lattice models amenable to exact numerical calculations, including Bose and spin models, with short- or long-range interactions. The approach also applies to higher dimensions, correlated fermions, and continuous models. We argue that it provides an alternative approach to standard pump-probe spectroscopic methods and discuss its advantages.

We study beyond-mean-field properties of interacting spin-1 Bose gases with synthetic Rashba-Dresselhaus spin-orbit coupling at low energies. We derive a many-body Hamiltonian following a tight-binding approximation in quasimomentum space, where the effective spin dependence of the collisions that emerge from spin-orbit coupling leads to dominant correlated tunneling processes that couple the different bound states. We discuss the properties of the spectrum of the derived Hamiltonian and its experimental signatures. In a certain region of the parameter space, the system becomes integrable, and its dynamics becomes analogous to that of a spin-1 condensate with spin-dependent collisions. Remarkably, we find that such dynamics can be observed in existing experimental setups through quench experiments that are robust against magnetic fluctuations.

We study the phononic collective modes of the pairing field and their corresponding signature in both the order-parameter and density response functions for a superfluid Fermi gas at all temperatures below $T_c$ in the collisionless regime. The spectra of collective modes are calculated within the Gaussian pair fluctuation approximation. We deal with the coupling of these modes to the fermionic continuum of quasiparticle-quasihole excitations by performing a nonperturbative analytic continuation of the pairing field propagator. At low temperature, we recover the known exponential temperature dependence of the damping rate and velocity shift of the Anderson-Bogoliubov branch. In the vicinity of $T_c$, we find analytically a weakly damped collective mode whose velocity vanishes with a critical exponent of $1/2$, and whose quality factor diverges logarithmically with $T_c-T$, thereby clarifying an existing debate in the literature [Andrianov and Popov, Theor. Math. Phys. 28, 829 (1976); Ohashi and Takada, J. Phys. Soc. Jpn. 66, 2437 (1997)]. A transition between these two phononic branches is visible at intermediary temperatures, particularly in the BCS limit where the phase-phase response function displays two maxima.

We address the problem of calculating the correlation functions of one-dimensional two-component gases with strong repulsive contact interactions. The model considered in this paper describes particles with fractional statistics and in appropriate limits reduces to the Gaudin-Yang model or the spinor Bose gas. In the case of impenetrable particles we derive a Fredholm determinant representation for the temperature-, time-, and space-dependent correlation functions which is very easy to implement numerically and constitutes the starting point for the analytical investigation of the asymptotics. Making use of this determinant representation and the solution of an associated Riemann-Hilbert problem we derive the low-energy asymptotics of the correlators in the spin-incoherent regime characterized by near ground-state charge degrees of freedom but a highly thermally disordered spin sector. The asymptotics present features reminiscent of spin-charge separation with the spin part exponentially decaying in space separation and oscillating with a period proportional to the statistics parameter, while the charge part presents scaling with anomalous exponents which cannot be described by any unitary conformal field theory. The momentum distribution and the Fourier transform of the dynamical Green's function are asymmetrical for arbitrary statistics, a direct consequence of the broken space-reversal symmetry. Due to the exponential decay the momentum distribution $n\left(k\right)$ at zero temperature does not present algebraic singularities but the tails obey the universal decay ${lim}_{k\to \pm \infty }n\left(k\right)\sim C/k^4$ with the amplitude $C$ given by Tan's contact. As a function of the statistics parameter the contact is a monotonic function reaching its minimum for the fermionic system and the maximum for the bosonic system.

We derive and apply a numerical model for the description of optically injected long-cavity Fabry-Pérot (FP) quantum-dot (QD) lasers, based on a multisection delay-algebraic-equation approach. In conjunction with experimental measurements, we characterize the multimode dynamics of the free-running laser as well as under external optical injection. We investigate the dynamics of the spatial hole burning (SHB) in the charge-carrier distribution, which is significant in QD lasers and is furthermore a driving mechanism for the emergence of multimode dynamics. In the injected laser, we focus on the transition between the locking regions of neighboring FP modes, which could not be described using traditional multimode rate-equation models. For very strong injection, the individual locking cones are found to converge. For intermediate injection strength, an additional dynamic boundary between the unlocked states is found in a narrow dynamical region in between two neighboring locking cones. This region is characterized by a further unlocking of all laser modes. Furthermore, we find the SHB to impose a threshold in the locking strength which must be overcome to lock a laser mode.

Two interacting atomic ensembles display a Dicke-like quantum phase transition above a critical coupling strength. We show that an ensemble-ensemble entanglement accompanies the quantum phase transition. We derive entanglement criteria which can witness the entanglement of the two interacting ensembles. We observe that all criteria are successful in the thermodynamic limit, while only the newly introduced ones (number-squeezing-like criteria) can witness the ensemble-ensemble entanglement for a finite number of particles. We also mention the implementations of these criteria to two-component condensate systems and nanoscale quantum plasmonics.

Performing homodyne detection at one port of a squeezed-state light interferometer and then binarizing the measurement data are important to achieve superresolving and supersensitive phase measurements. Here we propose an alternative data-processing technique by dividing the measurement quadrature into three bins (equivalent to a multi-outcome measurement), which leads to a higher improvement in the phase resolution and the phase sensitivity under realistic experimental conditions. Furthermore, we develop an alternative phase-estimation protocol based on a combination of the inversion estimators of each outcome and show that the estimator can saturate the Cramér-Rao lower bound, similar to the asymptotically unbiased maximum likelihood estimator.

We propose the use of the second-order magnetic-gradient-induced coupling between the nitrogen-vacancy center and the mechanical resonator for exploring the phonon-blockade effect in a hybrid system. This quantum effect essentially originates from the energy-level anharmonicity of the spin-mechanical system. Specifically, the second-order magnetic gradient could induce the two-phonon nonlinear coupling between spin qubits and phonons, which ultimately allows for the generation of phonon blockade. Moreover, this magnetically induced nonlinearity can be adjusted and enhanced to the strong-coupling regime. In this regime, we investigate the statistical characteristics of phonons by calculating the second-order correlation function numerically and analytically. In particular, we find that the antibunching effect of phonons is robust against the spin dephasing rate. This could provide an advantage and relax the required conditions for observing the phonon quantum effects from the perspective of experimental feasibility. Our work provides an alternative way, i.e., magnetically induced mechanical nonlinearity, to manipulate the mechanical quantum effects. Combined with the current quantum technologies, this study may extend the functionalities of hybrid systems and has potential applications in quantum information processing.

A concept for the realization of waveguide-based polarization beam splitters working over a wide spectral range is presented. The adiabatically evolving three-waveguide system is inspired by the quantum-mechanical stimulated Raman adiabatic passage process and involves waveguides with an anisotropic refractive index contrast. It is shown that an index contrast ratio of 5 is sufficient to obtain excellent efficiency and output polarization purity over a spectral range approximately equal to $350$ nm centered at a wavelength of 1550 nm. The center wavelength can be easily modified by tuning the parameters of the waveguides.

Complex vectorial light fields, nonseparable in their polarization and spatial degree of freedom, are of relevance in a wide variety of research areas encompassing microscopy, metrology, communication, and topological studies. Controversially, they have been suggested as analogs to quantum entanglement, raising fundamental questions on the relation between nonseparability in classical systems, and entanglement in quantum systems. We perform basis-independent tomography of arbitrary pure vectorial light fields using spatially resolved Stokes projections. Moreover, we propose and demonstrate that concurrence, as a nonseparability witness for any pure vectorial light field, can be extracted from global Stokes projections, without assessing the spatial degree of freedom.

A conceptual framework extending (time-independent) $\mathcal{PT}$-symmetric quantum mechanics into the time-dependent domain is presented. It is built upon a nontrivial time-dependent metric operator identified here and works for generic finite-dimensional non-Hermitian systems. All the ingredients of our framework, such as the time-dependent Hilbert space, the observable, and the measurement postulate, can be “realized” by means of dilating and reinterpreting the non-Hermitian system in question as a part of a larger Hermitian system. Aided by our metric operator, we formulate the concepts of stable and unstable phases for generic non-Hermitian systems and argue that they, respectively, generalize the notions of unbroken and broken phases in time-independent $\mathcal{PT}$-symmetric systems. Possible applications of our framework are illustrated with well-known examples in quantum thermodynamics.

Inelastic processes in low-energy ${\mathrm{Ca}}^{+}+\mathrm{H}$ and ${\mathrm{Ca}}^{2+}+{\mathrm{H}}^{-}$ collisions accounting for the fine structure of calcium ions are investigated. The present study is based on ab initio nonrelativistic potentials and on modification of the potentials by switching the representation from the $LS$ to the $JJ$ coupling scheme. The nuclear dynamical study is performed by the multichannel Landau-Zener approach for the collisional energy range ${10}^{-4}$ to 100 eV. The rate coefficients are calculated for the temperature range 1000 to 10 000 K. It is found that the largest rate coefficients correspond to the neutralization processes into the final channels ${\mathrm{Ca}}^{+}\left(4f{}^2{F}_{7/2}^{\circ }\right)$, ${\mathrm{Ca}}^{+}\left(6s{}^2{S}_{1/2}\right)$, ${\mathrm{Ca}}^{+}\left(5d{}^2{D}_{3/2,5/2}\right)$, ${\mathrm{Ca}}^{+}\left(6p{}^2{P}_{1/2,3/2}^{\circ }\right)$, and ${\mathrm{Ca}}^{+}\left(7s{}^2{S}_{1/2}\right)+\mathrm{H}\left(1s{}^2{S}_{1/2}\right)$, at a temperature of 6000 K they have values exceeding ${10}^{-8}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$, and the reaction mechanism for these processes corresponds to the long-range ionic-covalent interaction. The rate coefficients for the Ca II infrared triplet 849.8/854.2/866.2-nm transitions in collisions with H are found to be small. It is shown that accounting for the fine structure does not lead to a simple redistribution of rate coefficients obtained within the $LS$ coupling scheme between the fine-structure levels.

Photoelectron holography is a method that retrieves molecular structure information from photoelectron diffraction patterns generated by x-ray free-electron lasers, which have the promise of following dynamic molecular structure evolutions with angstrom spatial and femtosecond temporal resolutions (the so-called molecular movie). However, an additional phase is introduced when the photoelectron is scattered by an atom, and this scattering phase turns into a spatial error when the position of the atom is retrieved using a Fourier-type transform. We propose a method to remove, or greatly suppress, this error, with demonstrations using numerical examples.

On the basis of a quantum microscopic approach we study the cooperative effects induced by the dipole-dipole interaction in an ensemble of pointlike impurity centers located near a charged perfectly conducting surface. We analyze the simultaneous influence of the modified spatial structure of field modes near the conductive surface and the electric field on the transition spectrum of an excited atom inside an ensemble and on the radiation trapping. We show that the electric field modifies the cooperative Lamb shift, as well as the character of sub- and super-radiant decay. We also demonstrate that electro-optical effects in the presence of a surface are essentially different in comparison with those in free space. The nonmonotonic behavior of electro-optical effects in the presence of a surface with increasing of the electric field has been shown.

We study the $2\to 1$ process of electron-positron pair annihilation to a single photon in a plane-wave background. The probability of the process in a pulsed plane wave is presented, and a locally constant field approximation is derived and benchmarked against exact results. The stricter kinematics of annihilation (compared to the $1\to 2$ processes usually studied) leads to a stronger dependence on the incoming particle states. We demonstrate this by studying the effect that initial-state wave packets have on the annihilation probability. The effect of annihilation in a distribution of particles is studied by incorporating the process into Monte Carlo simulations.

The dynamics of a system that is correlated with an environment is almost always non-Markovian. Hence, it is important to characterize such correlations experimentally and witness them in physically realistic settings. One such setting is weak-field phase control where control is sought by the shaping of the phase of weak laser pulses. In this paper, we show how weak-field phase controllability can be combined with quantum preparations to witness initial correlations between the system and the environment. Furthermore, we show how this protocol can be applied to almost always predict violations of the quantum regression formula.

Physical implementation of scalable quantum architectures faces an immense challenge in the form of fragile quantum states. To overcome it, quantum architectures with fault tolerance are desirable. These are achieved currently by using a surface code along with a transversal gate set. This indicates the need for decomposition of universal $n$-qubit multicontrolled Toffoli ($n$-MCT) gates using a transversal gate set. Additionally, the transversal non-Clifford phase gate incurs high latency, which makes it an important factor to consider during decomposition. Additionally, the decomposition of a large MCT gate without ancillas presents an additional hurdle. In this paper, we address both of these issues by introducing the $\mathrm{Clifford}+Z_N$ gate library. We present an ancilla-free decomposition of MCT gates with linear phase depth and quadratic phase count. Furthermore, we provide a technique for decomposition of MCT gates in unit phase depth using the $\mathrm{Clifford}+Z_N$ library, albeit at the cost of ancillary lines and exponential phase count.