We present an optical picture of linear-optics superradiance, based on a single scattering event embedded in a dispersive effective medium composed by the other atoms. This linear-dispersion theory is valid at low density and in the single-scattering regime, i.e., when the exciting field is largely detuned. The comparison with the coupled-dipole model shows a perfect agreement for the superradiant decay rate. Then we use two advantages of this approach. First we make a direct comparison with experimental data, without any free parameter, and show a good quantitative agreement. Second, we address the problem of moving atoms, which can be efficiently simulated by adding the Doppler broadening to the theory. In particular, we discuss how to recover superradiance at high temperature.

We investigate the fundamental constraint on amplifying the asymmetry in quantum states with correlating catalysts. Here a correlating catalyst is a finite-dimensional auxiliary, which exactly preserves its reduced state while allowed to become correlated with the quantum system. Interestingly, we prove that under translationally invariant operations, uncorrelating catalysts in pure states are useless in any state transformation, while with a correlating catalyst, one can extend the set of accessible states from an initially asymmetric state. Moreover, we show that the power of a catalyst increases with its dimension, and further, with a large enough catalyst, a qubit state with an arbitrarily small amount of asymmetry can be converted to any mixed qubit state. In doing so, we build a bridge between two important results concerning the restrictions on coherence conversion, the no-broadcasting theorem and the catalytic coherence. Our results may also apply to the constraints on coherence evolution in quantum thermodynamics and to the distribution of timing information between quantum clocks.

We study two-dimensional quantum turbulence in miscible binary Bose-Einstein condensates in either a harmonic trap or a steep-wall trap through the numerical simulations of the Gross-Pitaevskii equations. The turbulence is generated through a Gaussian stirring potential. When the condensates have unequal intracomponent coupling strengths or asymmetric trap frequencies, the turbulent condensates undergo a dramatic decay dynamics to an interlaced array of vortex-antidark structures, a quasiequilibrium state, of like-signed vortices with an extended size of the vortex core. The time of formation of this state is shortened when the parameter asymmetry of the intracomponent couplings or the trap frequencies is enhanced. The corresponding spectrum of the incompressible kinetic energy exhibits two noteworthy features: (i) a $k^{-3}$ power law around the range of the wave number determined by the spin healing length (the size of the extended vortex core) and (ii) a flat region around the range of the wave number determined by the density healing length. The latter is associated with the small scale phase fluctuation relegated outside the Thomas-Fermi radius and is more prominent as the strength of intercomponent interaction approaches the strength of intracomponent interaction. We also study the impact of the intercomponent interaction to the cluster formation of like-signed vortices in an elliptical steep-wall trap, finding that the intercomponent coupling gives rise to the decay of the clustered configuration.

We explore the many-body phases of a two-dimensional Bose-Einstein condensate with cavity-mediated dynamic spin-orbit coupling. With the help of two transverse noninterfering, counterpropagating pump lasers and a single standing-wave cavity mode, two degenerate Zeeman sub-levels of the quantum gas are Raman coupled in a double-$\mathrm{\Lambda }$-configuration. Beyond a critical pump strength the cavity mode is populated via coherent superradiant Raman scattering from the two pump lasers, leading to the appearance of a dynamical spin-orbit coupling for the atoms. We identify three quantum phases with distinct atomic and photonic properties: the normal “homogeneous” phase, the superradiant “spin-helix” phase, and the superradiant “supersolid spin-density-wave” phase. The last exhibits an emergent periodic atomic density distribution with an orthorhombic centered rectangular-lattice structure due to the interplay between the coherent photon scattering into the resonator and the collision-induced momentum coupling. The transverse lattice spacing of the emergent crystal is set by the dynamic spin-orbit coupling.

We study the quantum motion of an impurity atom immersed in a Bose-Einstein condensate in arbitrary dimensions. It was shown, for all dimensions, that the Bogoliubov excitations of the Bose-Einstein condensate act as a bosonic bath for the impurity, where linear coupling is possible for a certain regime of validity, which was assessed only in one dimension. Here we present the detailed derivation of the ${\displaystyle d}$-dimensional Langevin equations that describe the quantum dynamics of the system, and of the associated generalized tensor that describes the spectral density in the full generality, and assesses the linear assumption in all dimensions. As results, we obtain, when the impurity is not trapped, the mean square displacement in all dimensions, showing that the motion is superdiffusive. We obtain also explicit expressions for the superdiffusive coefficient in the small and large temperature limits. We find that, in the latter case, the maximal value of this coefficient is the same in all dimensions, but is only reachable in one dimension, within the validity of the assumptions. We study also the behavior of the average energy and compare the results for various dimensions. In the trapped case, we study squeezing and find that the stronger position squeezing can be obtained in lower dimensions. We quantify the non-Markovianity of the particle's motion and find that it increases with dimensionality.

The generated magnitude of quadrature squeezing in a cavity-coupled ensemble, which is continuously driven using a coherent off-axis field, is theoretically explored. Using a truncated set of equations of motion derived from a Dicke Hamiltonian, steady-state quadrature squeezing of the cavity field is numerically calculated to approach a limit of $-3\mathrm{dB}$, while frequency-modulated quadrature squeezing approaches a limit of $-14\mathrm{dB}$, in the absence of pure dephasing and as a function of the ensemble's size and detuning. The impact of pure dephasing on steady-state quadrature squeezing is shown to be mitigated by increased detuning of the driving field, while frequency-modulated squeezing is only shielded in a regime where the cumulative coupling and driving rates are in excess of the pure-dephasing rate. Spin-squeezed entanglement is also calculated to occur simultaneously with weakly driven frequency-modulated quadrature squeezing.

The class of incoherent operations induces a preorder on the set of quantum pure states, defined by the possibility of converting one state into the other by transformations within the class. We prove that if two $n$-dimensional pure states are chosen independently according to the natural uniform distribution, then the probability that they are comparable vanishes as $n\to \infty$. We also study the maximal success probability of incoherent conversions and find an explicit formula for its large-$n$ asymptotic distribution. Our analysis is based on the observation that the extreme values (largest and smallest components) of a random point uniformly sampled from the unit simplex are distributed asymptotically as certain explicit homogeneous Markov chains.

We address the relation between absolutely maximally entangled (AME) states and quantum- maximum-distance-separable (QMDS) codes by constructing whole families of QMDS codes from AME states that have stabilizer representations. We introduce a generic reduction-friendly form for the generator set of the stabilizer representation of an AME state, from which the stabilizer form for children codes, all QMDS, can be obtained. Our method would work for relevant high-dimensional codes as well as qubit-based codes. We then relate this to optimal codes for one-way quantum repeaters, by minimizing the short-term infrastructure cost as well as the long-term running cost of such quantum repeaters. This would allow us to obtain the optimal QMDS code, derived from an AME parent state, that can be used in such quantum repeaters.

We have developed an all-particle Fock-space relativistic coupled-cluster method to calculate the properties of two-valence atoms and ions. Using the method we compute the properties associated with a hyperfine-induced ${}^1{S}_0\to {}^3{P}_0^o$ clock transition in ${\mathrm{Al}}^{+}$. Our result of the ${}^3{P}_0^o$ metastable-state lifetime, $20.20\pm 0.91$ s, is in excellent agreement with the experimental value, $20.60\pm 1.4$ s [T. Rosenband et al., Phys. Rev. Lett. 98, 220801 (2007)]. Our studies show that the contributions from the triple excitations, and the corrections from the Breit interaction and QED effects, are essential to obtain accurate clock properties in ${\mathrm{Al}}^{+}$.

We generalize the formalism proposed by Dalibard, Dupont-Roc, and Cohen-Tannoudji (the DDC formalism) to the fourth order of the coupling constant, which can be used to study the interatomic interaction of two ground-state atoms coupled with the vacuum scalar fields. We show that the interatomic potential can be attributed to the joint effect of both vacuum fluctuations and the radiation reaction of atoms. Remarkably, the formulas we derived for the contributions of vacuum fluctuations and the radiation reaction to the interatomic potential upon which future research on fourth-order effects in particular circumstances can be based differ from those in the existing literature [Phys. Rev. D 95, 085014 (2017)].

The so-called quantum Cheshire Cat is a scenario where a photon, identified with a cat, and a component of its polarization, identified with the grin of that cat, are separated. We observe that the same techniques can be used to separate two orthogonal components of polarization of a photon, on an average. We identify these polarization components of the photon as the grin and snarl of the cat for ease of comprehension. A gedanken experiment is presented in which we simultaneously tune the input polarizations of the photon in the two arms of a Mach-Zehnder interferometer. It is noted that for two particular choices of photon polarization, the presence of the two components gets reversed in the two arms. This reversal of the grin and the snarl occurs before the polarization components even interact with the tuners, i.e., before the choice of which arm each should be in is made.

The computational quantum field theory (CQFT) is applied to study the dependence of the total EPP number on the time interval under the spatially localized double cosine-Gaussian pulse and the alternating-sign double-Gaussian pulse. The total EPP number damply oscillates with the time interval, and the oscillation frequency is about the energy gap ($2m{c}^2$) for all of the scenarios. This characteristic oscillation of the total EPP number is consistent with a formula, which is related to the amplitude mode in the BCS superconductors. Besides, we find that the Ramsey interference effect is not responsible for the characteristic oscillation by studying the double-Gaussian pulse with the same sign. Finally, when the favorable time interval is applied, the EPP number is much larger than the sum of the EPP number obtained in two single pulses. The favorable time interval mainly depends on the pulse duration and the carrier envelope phase (the quantity in cosine-Gaussian pulse).

Quantum error mitigation (QEM) has been proposed as an alternative method of quantum error correction to compensate errors in quantum systems without qubit overhead. While Markovian gate errors on digital quantum computers have been mainly considered previously, it is indispensable to discuss a relationship between QEM and non-Markovian errors because non-Markovian noise effects inevitably exist in most of the solid-state systems. In this work, we investigate the QEM for non-Markovian noise, and show that there is a clear relationship between costs for QEM and non-Markovian measures. As examples, we show several non-Markovian noise models to bridge a gap between our theoretical framework and concrete physical systems. This discovery may help in designing better QEM strategies for realistic quantum devices with non-Markovian environments.

Driving an ion at a motional sideband transition induces the Jaynes-Cummings (JC) interaction. This JC interaction creates an anharmonic ladder of JC eigenstates, resulting in the suppression of phonon hopping due to energy conservation. Here, we realize phonon blockade in the presence of multiple local phonons in a trapped-ion chain. This work constitutes a concrete study on the evolution of multiple local phonons with or without phonon blockade.

Attosecond metrology can directly measure attosecond emission time of photoexcited electrons from matter, providing unprecedented understanding of transition processes of electrons from bound to continuum states. However, some fundamental details of the electron dynamics in the entire emission process upon photoexcitation still remain debatable or unknown. The photoemission time delays deduced from attosecond streaking spectroscopy originate from photoelectron propagation in the coupled Coulomb-laser fields, encoding the spatial and spectral information of electrons upon photoexcitation. Here we demonstrate that attosecond photoemission delays can be used to image picometer-resolved photoemission position via a classical model. The electronic dynamics in the laser-assisted single-photon ionization process is fully captured by a quantum path-integral model. We trace the imaged photoemission position to the average position of spatially coherent superposition of electron waves upon photoexcitation and, in particular, predict emission position coinciding with the orbital radius of the ground state of hydrogen-like atoms, in contrast with previous predictions.

We consider ultracold atoms trapped in a toroidal trap with an azimuthal lattice for utility as a macroscopic simulator of quantum optics phenomena. We examine the dynamics induced by the adiabatic introduction of the lattice that serves to couple the normal modes as an analog of a laser field coupling electronic states. The system is found to display two distinct behaviors, manifest in the angular momentum—coherent oscillation and self-trapping—reminiscent of nonlinear dynamics yet not requiring interatomic interactions. The choice is set by the interplay of discrete parameters, the specific initial mode, and the periodicity of the lattice. However, rotation can cause continuous transition between the two regimes, causing periodic quenches and revivals in the oscillations as a function of the angular velocity. Curiously, the impact of rotation is determined entirely by the energy spectrum in the absence of the lattice, a feature that can be attributed to adiabaticity. We assess the effects of varying the lattice parameters and consider applications in rotation sensing.

The tractability of the Sachdev-Ye-Kitaev (SYK) model at the large $N$ limit makes it ideal to theoretically study its chaotic non-Fermi liquid behavior and holographic duality properties. We show that the complex SYK Hamiltonian emerges from a system of spinless itinerant fermionic atoms in an optical kagome lattice with a strong disorder. We discuss the regimes supporting flat band spectra in a kagome lattice, where the system can be nondispersive. Random interaction between nondispersive fermions is induced due to randomly distributed immobile impurities in the optical lattice, that impede the presence of itinerant fermions at their locations. We show that the proposed setup represents a maximally chaotic system and is a reliable experimental platform to realize the SYK model and study its exotic behavior. We show that the velocity distribution of the released fermions is a sensitive probe of the many-body Wigner-Dyson spectral density of states while the averaged many-body Loschmidt echo scheme can measure two-point out-of-time-ordered correlation functions of the SYK system.

We present the theory of modulation instability induced by spectrally dependent losses (optical filters) in passive driven nonlinear fiber ring resonators. Starting from an Ikeda map description of the propagation equation and boundary conditions, we derive a mean-field model—a generalized Lugiato-Lefever equation—which reproduces with great accuracy the predictions of the map. The effects on instability gain and comb generation of the different control parameters such as dispersion, cavity detuning, filter spectral position, and bandwidth are discussed.

We study a generalized Aubry-André model that obeys $\mathcal{PT}$ symmetry. We observe a robust $\mathcal{PT}$-symmetric phase with respect to system size and disorder strength, where all eigenvalues are real despite the Hamiltonian being non-Hermitian. This robust $\mathcal{PT}$-symmetric phase can support an Anderson localization transition, giving a rich phase diagram as a result of the interplay between disorder and $\mathcal{PT}$ symmetry. Our model provides a perfect platform to study disorder-driven localization phenomena in a $\mathcal{PT}$-symmetric system.