Pattern formation of atoms in high-finesse optical resonators results from the mechanical forces of light associated with superradiant scattering into the cavity mode. It occurs when the laser intensity exceeds a threshold value such that the pumping processes counteract the losses. We consider atoms driven by a laser and coupling with a mode of a standing-wave cavity and describe their dynamics with a Fokker-Planck equation, in which the atomic motion is semiclassical but the cavity field is a full quantum variable. The asymptotic state of the atoms is a thermal state, whose temperature is solely controlled by the detuning between the laser and the cavity frequency and by the cavity loss rate. From this result we derive the free energy and show that in the thermodynamic limit self-organization is a second-order phase transition. The order parameter is the field inside the resonator to which one can associate a magnetization in analogy to ferromagnetism, the control field is the laser intensity, but the steady state is intrinsically out of equilibrium. In the symmetry-broken phase, quantum noise induces jumps of the spatial density between two ordered patterns: We characterize the statistical properties of this temporal behavior at steady state and show that the thermodynamic properties of the system can be extracted by detecting the light at the cavity output. The results of our analysis are in full agreement with previous studies; we extend them by deriving a self-consistent theory which is valid also when the cavity field is in the shot-noise limit and elucidate the nature of the self-organization transition.

We theoretically analyze the effects of two primary mechanisms of residual amplitude modulation, estimate the resulting frequency instabilities, and discuss relevant experimental countermeasures, providing useful information that are beneficial for the development of ultrastable optical oscillators as well as many precision experiments relying on stable lasers. A Pound-Drever-Hall signal comprising contributions from the birefringence of the electro-optic crystal is derived and used to examine the birefringence-related amplitude modulation and the resultant frequency offset in terms of various experimental parameters. The combined effect of the crystal birefringence and pararsitic étalons is further investigated by dividing the étalons into three representative categories according to their locations in the optical path. The analysis shows that introducing a resonant optical cavity only scales the birefringence-generated amplitude modulation by a constant, thereby lending strong support to the active control scheme using a separate detection path. When a parasitic étalon is added, the active control scheme can still suppress the resultant instability except for the parasitic étalon that is located closely in front of the optical cavity. In this case the étalon produces rather large frequency instability and therefore should be avoided. In addition, numerical calculations are performed to assess the impact of a special situation where the front and end surfaces of an ultrastable optical cavity are potential sources of the parasitic étalon that can strongly couple with the cavity.

We perform saturated absorption spectroscopy on the $D_2$ line for room temperature rubidium atoms immersed in magnetic fields within the 0.05–0.13 T range. At those medium-high field values the hyperfine structure in the excited state is broken by the Zeeman effect, while in the ground-state hyperfine structure and Zeeman shifts are comparable. The observed spectra are composed by a large number of absorption lines. We identify them as saturated absorptions on two-level systems, on three-level systems in a $\mathsf{V}$ configuration, and on four-level systems in an $\mathsf{N}$ or double-$\mathsf{N}$ configuration where two optical transitions not sharing a common level are coupled by spontaneous emission decays. We analyze the intensity of all those transitions within a unified simple theoretical model. We concentrate our attention on the double-$\mathsf{N}$ crossovers signals whose intensity is very large because of the symmetry in the branching ratios of the four levels. We point out that these structures, present in all alkali-metal atoms at medium-high magnetic fields, have interesting properties for electromagnetically induced transparency and slow light applications.

Nonperturbative calculation of QED processes involving a strong electromagnetic field, especially provided by strong laser facilities at present and in the near future, generally resorts to the Furry picture with the use of analytical solutions of particle dynamical equations, such as the Klein-Gordon equation and Dirac equation. However, only for limited field configurations such as a plane-wave field could the equations be solved analytically. Studies have shown significant interest in QED processes in a strong field composed of two counterpropagating laser waves, but the exact solution in such a field is out of reach. In this paper, inspired by the observation of the structure of the solutions in a plane-wave field, we develop a method and obtain the analytical solution for the Klein-Gordon equation and equivalently the action function of the solution for the Dirac equation in this field, under a largest dynamical parameter condition that there exists an inertial frame in which the particle free momentum is far larger than the other field dynamical parameters. The applicable range of the solution is demonstrated and its validity is proven clearly. The result has the advantages of Lorentz covariance, clear structure, and close similarity to the solution in a plane-wave field, and thus favors convenient application.

The quantum speed limit sets the minimum time required to transfer a quantum system completely into a given target state. At shorter times the higher operation speed results in a loss of fidelity. Here we quantify the trade-off between the fidelity and the duration in a system driven by a time-varying control. The problem is addressed in the framework of Hilbert space geometry offering an intuitive interpretation of optimal control algorithms. This approach leads to a necessary criterion for control optimality applicable as a measure of algorithm convergence. The time fidelity trade-off expressed in terms of the direct Hilbert velocity provides a robust prediction of the quantum speed limit and allows one to adapt the control optimization such that it yields a predefined fidelity. The results are verified numerically in a multilevel system with a constrained Hamiltonian and a classification scheme for the control sequences is proposed based on their optimizability.

We propose a test of local realism based on correlation measurements of continuum valued functions of positions and momenta, known as modular variables. The Wigner representations of these observables are bounded in phase space and, therefore, the associated inequality holds for any state described by a non-negative Wigner function. This agrees with Bell's remark that positive Wigner functions, serving as a valid probability distribution over local (hidden) phase-space coordinates, do not reveal nonlocality. We construct a class of entangled states resulting in a violation of the inequality and thus truly demonstrate nonlocality in phase space. The states can be realized through grating techniques in spacelike separated interferometric setups. The nonlocality is verified from the spatial correlation data that is collected from the screens.

We present a nonperturbative computation of the equation of state of polarized, attractively interacting, nonrelativistic fermions in one spatial dimension at finite temperature. We show results for the density, spin magnetization, magnetic susceptibility, and Tan's contact. We compare with the second-order virial expansion, a next-to-leading-order lattice perturbation theory calculation, and interpret our results in terms of pairing correlations. Our lattice Monte Carlo calculations implement an imaginary chemical potential difference to avoid the sign problem. The thermodynamic results on the imaginary side are analytically continued to obtain results on the real axis. We focus on an intermediate- to strong-coupling regime, and cover a wide range of temperatures and spin imbalances.

We examine the properties of a family of defects called hyperbolic disclinations, and discuss their possible use for the design of perfect optical absorbers. In hyperbolic metamaterials, the ratio of ordinary and extraordinary permittivities is negative, which leads to an effective metric of Kleinian signature (two timelike coordinates). Considering a disclination in the hyperbolic nematic host matrix, we show that the timelike geodesics are Poinsot spirals, i.e., whatever the impact parameter of an incident light beam, it is confined and whirls about the defect core. The trapping effect does not require light to be coherent. This property also remains in the wave formalism, which may be the sign for many potential applications.

The properties of a balanced two-component Fermi gas in a one-dimensional harmonic trap are studied by means of the coupled-cluster method. For few fermions we recover the results of exact diagonalization, yet with this method we are able to study much larger systems. We compute the energy, the chemical potential, the pairing gap, and the density profile of the trapped clouds, smoothly mapping the crossover between the few-body and many-body limits. The energy is found to converge surprisingly rapidly to the many-body result for every value of the interaction strength. Many more particles are instead needed to give rise to the nonanalytic behavior of the pairing gap, and to smoothen the pronounced even-odd oscillations of the chemical potential induced by the shell structure of the trap.

We present a scheme for a compact rubidium cold-atom clock which performs diffuse light cooling, microwave interrogation, and detection of the clock signal in a cylindrical microwave cavity. The diffuse light is produced by laser light reflection at the inner surface of the microwave cavity. The pattern of the injected laser beams is specially designed to accumulate the majority of the cold atoms in the center of the microwave cavity. Microwave interrogation of the cold atoms in the cavity leads to Ramsey fringes, which have a linewidth of $24.5$ Hz with a contrast of $95.6\%$ when the free evolution time is 20 ms. Recently, a frequency stability of $7.3\times {10}^{-13}{\tau }^{-1/2}$ has been achieved. The scheme of this physical package can largely reduce the cold-atom clock complexity and increase clock performance.

We propose a scheme for quantum estimation by means of parametric amplification in circuit quantum electrodynamics. The modulation of a superconducting quantum interference device interrupting a superconducting waveguide transforms an initial thermal two-mode squeezed state in such a way that the new state is sensitive to the features of the parametric amplifier. We find the optimal initial parameters which maximize the quantum Fisher information (QFI). To achieve a large number of independent measurements we propose using an array of noninteracting resonators. We show that the combination of both large QFI and a large number of measurements enables, in principle, the use of this setup for quantum metrology applications.

A conventional quantum phase transition (QPT) not only occurs at zero temperature, but also exhibits finite-temperature quantum criticality. Motivated by the discovery of the pseudo-Hermiticity of non-Hermitian systems, we explore the finite-temperature quantum criticality in a non-Hermitian $\mathcal{PT}$-symmetric Ising model. We present the complete set of exact eigenstates of the non-Hermitian Hamiltonian, based on which the mixed-state fidelity in the context of biorthogonal bases is calculated. Analytical and numerical results show that the fidelity approach to finite-temperature QPT can be extended to the non-Hermitian Ising model. This paves the way for experimental detection of quantum criticality in a complex-parameter plane.

We investigate the effect of disorder on the transfer of quantum states across a one-dimensional lattice with varying levels of control resources. We find that the application of properly designed control signals, even when applied only to the two ends of the lattice, allows perfect state transfer up to disorder strengths that would not allow a generic quantum state to propagate the length of the lattice. At sufficiently large disorder strengths, however, the local control signals fail to send the quantum state from one end of the system to the other end. Our results shed light on the interplay between disorder and controlled transport in one-dimensional systems.

We investigate non-Markovianity measure using two-time correlation functions for open quantum systems. We define non-Markovianity measure as the difference between the exact two-time correlation function and the one obtained from quantum regression theorem in the Born-Markov approximation. Such non-Markovianity can easily be measured in experiments. We found that the non-Markovianity dynamics in different time scale crucially depends on the system-environment coupling strength and other physical parameters such as the initial temperature of the environment and the initial state of the system. In particular, we obtain the short-time and long-time behaviors of non-Markovianity for different spectral densities. We find that the thermal fluctuation always reduce the non-Markovian memory effect. Also, the non-Markovianity measure shows nontrivial initial state dependence in different time scales.

A two-dimensional discrete-time quantum walk (DTQW) can be realized by alternating a two-state DTQW in one spatial dimension followed by an evolution in the other dimension. This was shown to reproduce a probability distribution for a certain configuration of a four-state DTQW on a two-dimensional lattice. In this work we present a three-state alternate DTQW with a parametrized coin-flip operator and show that it can produce localization that is also observed for a certain other configuration of the four-state DTQW and nonreproducible using the two-state alternate DTQW. We will present two limit theorems for the three-state alternate DTQW. One of the limit theorems describes a long-time limit of a return probability, and the other presents a convergence in distribution for the position of the walker on a rescaled space by time. We find that the spatial entanglement generated by the three-state alternate DTQW is higher than that by the four-state DTQW. Using all our results, we outline the relevance of these walks in three-level physical systems.

In the counterfactual cryptography scheme proposed by Noh, the sender Alice probabilistically transmits classical information to the receiver Bob without the physical travel of a particle. Here we generalize this idea to the distribution of quantum entanglement. The key insight is to replace their classical input choices with quantum superpositions. We further show that the scheme can be generalized to counterfactually distribute multipartite cat states.

We analyze a model for fault-tolerant quantum computation with low overhead suitable for situations where the noise is biased. The basis for this scheme is a gadget for the fault-tolerant preparation of magic states that enable universal fault-tolerant quantum computation using only Clifford gates that preserve the noise bias. We analyze the distillation of $|T\rangle$-type magic states using this gadget at the physical level, followed by concatenation with the 15-qubit quantum Reed-Muller code, and comparing our results with standard constructions. In the regime where the noise bias (rate of Pauli $Z$ errors relative to other single-qubit errors) is greater than a factor of 10, our scheme has lower overhead across a broad range of relevant noise rates.

We use a picosecond frequency-doubled mode-locked titanium sapphire laser to generate a frequency comb at 431 nm in order to probe the $\left(3s^2\right){}^1{S}_0\to \left(3s3d\right){}^1{D}_2$ transition in atomic magnesium. Using a second, self-referenced femtosecond frequency comb, the absolute transition frequency and the ${}^{24}\mathrm{Mg}$ and ${}^{26}\mathrm{Mg}$ isotope shift is determined relative to a global-positioning-system-referenced hydrogen maser. Our result for the transition frequency of the main isotope ${}^{24}\mathrm{Mg}$ of $1391128606.14\left(12\right)$ MHz agrees with previous measurements and reduces its uncertainty by four orders of magnitude. For the isotope shift we find $\delta {\nu }^{26,24}=3915.13\left(39\right)$ MHz. Accurate values for transition frequencies in Mg are relevant in astrophysics and to test atomic structure calculations.

We derive a nonequilibrium finite-temperature kinetic theory for a binary mixture of two interacting atomic Bose-Einstein condensates and use it to explore the degree of hydrodynamicity attainable in realistic experimental geometries. Based on the standard separation-of-time-scales argument of kinetic theory, the dynamics of the condensates of the multicomponent system are shown to be described by dissipative Gross-Pitaevskii equations self-consistently coupled to corresponding quantum Boltzmann equations for the noncondensate atoms: On top of the usual mean-field contributions, our scheme identifies a total of eight distinct collisional processes, whose dynamical interplay is expected to be responsible for the system's equilibration. In order to provide their first characterization, we perform a detailed numerical analysis of the role of trap frequency and geometry on collisional rates for experimentally accessible mixtures of ${}^{87}\mathrm{Rb}-{}^{41}\mathrm{K}$ and ${}^{87}\mathrm{Rb}-{}^{85}\mathrm{Rb}$, discussing the extent to which the system may approach the hydrodynamic regime with regard to some of those processes as a guide for future experimental investigations of ultracold Bose gas mixtures.