We study the quantum dynamics of many-body arrays of two-level atoms in a driven cavity subject to collective decay and interactions mediated by the cavity field. We work in the bad cavity limit accessible, for example, using long-lived electronic clock states of alkaline-earth atoms, for which the bare atomic linewidth is much less than the cavity linewidth. In the absence of interactions, our system reduces to previously studied models of collective fluorescence. We show that while interactions do not qualitatively change the steady-state properties they lead to a drastic change in the dynamical properties. We find that, for some intervals of driving strengths, the system shows two very distinct types of transient behaviors that depend on the initial state of the system. In particular, there is a parameter regime where the system features oscillatory dynamics with a period of oscillation that becomes much shorter than the duration of the overall transient dynamics as the atom number increases. We use both mean-field and exact numerical calculations of the quantum system to investigate the dynamics.

We describe theoretically the quasi-one-dimensional transverse spreading of a light beam propagating in a nonlinear optical material in the presence of a uniform background light intensity. For short propagation distances the pulse can be described within a nondispersive (geometric optics) approximation by means of Riemann's approach. For larger distances, wave breaking occurs, leading to the formation of dispersive shocks at both edges of the beam. We describe this phenomenon within Whitham modulation theory, which yields excellent agreement with numerical simulations. Our analytic approach makes it possible to extract the leading asymptotic behavior of the parameters of the shock, setting up the basis for a theory of nondissipative weak shocks.

Quantum inseparabilities can be classified into three inequivalent forms: entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Bell-nonlocal states form a strict subset of EPR steerable states which also form a strict subset of entangled states. Recently, EPR steerable states have been shown to be fundamental resources for one-sided device-independent quantum information processing tasks and, hence, identification of EPR steerable states becomes important from foundational as well as informational theoretic perspectives. In the present paper, we propose a criterion to detect whether a given two-qubit state is EPR steerable. From an arbitrary given two-qubit state, another two-qubit state is constructed in such a way that the given state is EPR steerable if the new constructed state is entangled. Hence, EPR steerability of an arbitrary two-qubit state can be detected by detecting entanglement of the newly constructed state. Apart from providing a distinctive way to detect EPR steering without using any steering inequality, the present paper also provides an alternative way to avoid locality loopholes in EPR steering tests and to reduce the “complexity cost” present in experimentally detecting EPR steering. We also generalize our criteria to detect EPR steering of higher dimensional quantum states. Finally, we illustrate our result by using our proposed technique to detect EPR steerability of various families of mixed states.

The complex eigenvalues of some non-Hermitian Hamiltonians, e.g., parity-time-symmetric Hamiltonians, come in complex-conjugate pairs. We show that for non-Hermitian scattering Hamiltonians (of a structureless particle in one dimension) possessing one of four certain symmetries, the poles of the $S$-matrix eigenvalues in the complex momentum plane are symmetric about the imaginary axis, i.e., they are complex-conjugate pairs on the complex-energy plane. This applies even to states which are not bounded eigenstates of the system, i.e., antibound or virtual states, resonances, and antiresonances. The four Hamiltonian symmetries are formulated as the commutation of the Hamiltonian with specific antilinear operators. Example potentials with such symmetries are constructed and their pole structures and scattering properties are calculated.

Nonclassical correlations beyond entanglement might provide a resource in quantum information tasks, such as quantum computation or quantum metrology. Quantum discord is a measure of nonclassical correlations to which entanglement belongs as a subset. Exploring the operational meaning of quantum discord as a resource in quantum information processing tasks, such as quantum metrology, is of essential importance to our understanding of nonclassical correlations. In our recent work [Phys. Rev. A 98, 012115 (2018)], we considered a protocol—which we call the greedy local thermometry protocol—for estimating the temperature of thermal equilibrium states from local measurements, elucidating the role of diagonal discord in enhancing the protocol sensitivity in the high-temperature limit. In this paper, we extend our results to a general greedy local parameter estimation scenario. In particular, we introduce a quantum discord—which we call discord for local metrology—to quantify the nonclassical correlations induced by the local optimal measurement on the subsystem. We demonstrate explicitly that discord for local metrology plays a role in sensitivity enhancement in the high-temperature limit by showing its relation to loss in quantum Fisher information. In particular, it coincides with diagonal discord for estimating a linear coupling parameter.

We describe an isoelectronic differential apparatus designed to observe the influence on the Casimir force of the Mott-Anderson metal-insulator transition in doped semiconductors. Alternative theories of dispersion forces lead to different predictions for this effect. The investigation of this problem by standard apparatus, based on absolute measurements of the Casimir force, is very difficult because the effect is small in the region of submicron separations, where the Casimir force can be measured precisely. The differential apparatus described here is immune by design to several sources of error that blur the interpretation of Casimir experiments, such as electrostatic patches, inaccurate determination of plates separation, surface roughness, and errors in the optical data. With the help of the proposed setup, it should be possible to establish conclusively which among the alternative theories of the Casimir effect for semiconducting test bodies is correct.

We study the breakdown of the nonrelativistic approximation in the multiphoton ionization of atomic hydrogen by some intense x-ray laser pulse, in a regime where the dipole approximation is no longer valid. To this end, both the time-dependent Dirac equation as well as its nonrelativistic counterpart, the time-dependent Schrödinger equation, are solved within an ab initio numerical framework. It is demonstrated that a recently developed semirelativistic Schrödinger equation for superintense laser fields [Lindblom et al., Phys. Rev. Lett. 121, 253202 (2018)] yields results in excellent agreement with the fully relativistic treatment. The semirelativistic equation is then used in an investigation of the role of higher-order beyond-dipole corrections to the laser-matter interaction. The result of the present study can be summarized into two main findings: (1) relativistic effects predict a blueshift of the multiphoton ionization spectrum, and (2) higher-order beyond dipole corrections (beyond the leading-order term) indicate a corresponding redshift of the photoelectron spectrum. However, the two shifts turn out to be of the same order of magnitude, effectively leading to a net cancellation of their respective contributions. This apparent cancellation effect raises an important question: Is the distinction between relativistic blueshifts and higher-order beyond dipole redshifts meaningful from an experimental point of view? The result of the present study indicates that the answer is negative because the two effects nonetheless cannot be measured separately. Therefore, instead, we suggest that the present findings should merely be taken as a demonstration that caution should be exercised when higher-order beyond-dipole and relativistic corrections are to be taken into account in approximation schemes in the modeling of superintense laser-matter interactions.

We consider a system of interacting bosons in one dimension at a two-body resonance. This system, which is weakly interacting, is known to give rise to effective three-particle interactions, whose dynamics is similar to that of a two-dimensional Bose gas with two-body interactions, and exhibits an identical scale anomaly. We consider the experimentally relevant scenario of a harmonically trapped system. We solve the three-body problem exactly and evaluate the shifts in the frequency of the lowest compressional mode with respect to the dipole mode, and find that the effect of the anomaly is to increase the mode's frequency. We also consider the weak-coupling regime of the trapped many-boson problem and find, within the local density approximation, that the frequency of the lowest compressional mode is also shifted upward in this limit. Moreover, the anomalous frequency shifts are enhanced by the higher particle number to values that should be observable experimentally.

The Mielke checkerboard is known to be one of the simplest two-band lattice models exhibiting an energetically flat band that is in touch with a quadratically dispersive band in the reciprocal space, i.e., its flat band is not isolated. Motivated by the growing interest in understanding the origins of flat-band superfluidity in various contexts, here we provide an in-depth analysis showing how the mean-field BCS correlations prevail in this particular model. Our work reveals the quantum-geometric origin of flat-band superfluidity through uncovering the leading role by a band-structure invariant, i.e., the so-called quantum metric tensor of the single-particle bands, in the inverse effective mass tensor of the Cooper pairs.

We consider the phase transition dynamics of a trapped Bose-Einstein condensate subject to Raman-type spin-orbit coupling. By tuning the coupling strength the condensate is taken through a second-order phase transition into an immiscible phase. We observe the domain wall defects produced by a finite speed quench is described by the Kibble-Zurek mechanism, and quantify a power-law behavior for the scaling of domain number and formation time with the quench speed.

We consider an optical cavity enclosed by a freely moving mirror attached to a spring and we study the quantum friction effect exerted by the dynamical Casimir emission on the mechanical motion of the mirror. Observable signatures of this simplest example of backreaction effect are studied in both the ring-down oscillations of the mirror motion and in its steady-state motion under a monochromatic force. Analytical expressions are found in simple yet relevant cases and compared to complete numerical solution of the master equation. In order to overcome the experimental difficulties posed by the weakness of the backreaction effect in current setups, a promising circuit-QED device allowing for the observation of an analog backreaction effect with state-of-the-art technology is proposed and theoretically characterized.

We consider a complete description of a multi-mode bosonic quantum state in the coherent-state basis (which in this paper is denoted as the “$K$” function), which—up to a phase—is the square root of the well-known Husimi $Q$ representation. We express the $K$ function of any $N$-mode Gaussian state as a function of its covariance matrix and displacement vector, and also that of a general continuous-variable cluster state in terms of the modal squeezing and graph topology of the cluster. This formalism lets us characterize the non-Gaussian state left over when one measures a subset of modes of a Gaussian state using photon number resolving detection, the fidelity of the obtained non-Gaussian state with any target state, and the associated heralding probability, all analytically. We show that this probability can be expressed as a Hafnian, reinterpreting the output state of a circuit claimed to demonstrate quantum supremacy termed Gaussian boson sampling. As an example application of our formalism, we propose a method to prepare a two-mode coherent-cat-basis Bell state with fidelity close to unity and success probability that is fundamentally higher than that of a well-known scheme that splits an approximate single-mode cat state—obtained by photon number subtraction on a squeezed vacuum mode—on a balanced beam splitter. This formalism could enable exploration of efficient generation of cat-basis entangled states, which are known to be useful for quantum error correction against photon loss.

Quantum photonics has demonstrated its potential for enhanced sensing. Current sources of quantum light states tailored to measuring allow one to monitor phenomena evolving on timescales of second order. These are characteristic of product accumulation in chemical reactions of technological interest, in particular those involving chiral compounds. Here we adopt a quantum multiparameter approach to investigate the dynamic process of sucrose acid hydrolysis as a test bed for such applications. The estimation is made robust by monitoring different parameters at once.

We develop a concept for a waveguide that exploits spatial control of nonlinear surface-polaritonic waves. Our scheme includes an optical cavity with four-level $N$-type atoms in a lossless dielectric placed above a negative-index metamaterial layer. We propose exciting a polaritonic Akhmediev breather at a certain position of the interface between the atomic medium and the metamaterial by modifying laser-field intensities and detunings. Furthermore, we propose generating position-dependent polaritonic frequency combs by engineering widths of the electromagnetically induced transparency window commensurate with the surface-polaritonic modulation instability. Therefore, this waveguide acts as a high-speed polaritonic modulator and position-dependent frequency-comb generator, which can be applied to compact photonic chips.

Quantum information leverages correlations between spacelike separated parties in order to perform useful tasks such as secure communication and randomness certification. Nevertheless, not much is known about the intricate geometric features of the set quantum correlators. In this paper we study the structure of the set of quantum correlators using semidefinite programming, more precisely the boundary, extreme, and exposed points. We obtain quantum Bell inequalities characterizing a certain class of bipartite scenarios. In the case of two dichotomic measurements, extremal quantum correlators coincide with the correlators that uniquely determine the state and measurement operators, a property known as self-testing. We illustrate the usefulness of our theoretical findings with many examples and extensive computational work.

Photonic quantum memory, such as an atomic frequency comb (AFC), is essential to make photonic quantum computation and long distance quantum communication scalable and feasible. In standard AFC the frequency of different atoms must be stable relative to each other which presents difficulties in realizing the quantum memory. Here we propose a quantum memory using an intra-atomic frequency comb which does not require frequency stabilization. We show that the transitions between two degenerate energy levels of a single atom can be used to construct the frequency comb. The spacing between the teeth of the comb is controlled by applying an external magnetic field. Since the frequency comb is constructed from individual atoms, these atoms can be used alone or in ensembles to realize the quantum memory. Furthermore, the ensemble based quantum memory with intra-AFC is robust against Doppler broadening which makes it useful for high-temperature quantum memory. As an example, we numerically show the intra-AFC in cesium atoms and demonstrate a photon echo which is essential for quantum memory.

We generalize a quantum communication protocol introduced by Bartlett et al. [New J. Phys. 11, 063013 (2009)], in which two parties communicating do not share a classical reference frame, to the case where changes of their reference frames form a one-dimensional noncompact Lie group. Alice sends to Bob the state ${\rho }_R\otimes {\rho }_S$, where ${\rho }_S$ is the state of the system Alice wishes to communicate and ${\rho }_R$ is the state of an ancillary system serving as a token of her reference frame. Because Bob is ignorant of the relationship between his reference frame and Alice's, he will describe the state ${\rho }_R\otimes {\rho }_S$ as an average over all possible reference frames. Bob measures the reference token and applies a correction to the system Alice wished to communicate conditioned on the outcome of the measurement. The recovered state ${\rho }_S^{\prime }$ is decohered with respect to ${\rho }_S$, the amount of decoherence depending on the properties of the reference token ${\rho }_R$. We present an example of this protocol when Alice and Bob do not share a reference frame associated with the one-dimensional translation group and use the fidelity between ${\rho }_S$ and ${\rho }_S^{\prime }$ to quantify the success of the recovery operation.

In this work, we develop a method to design control pulses for fixed-frequency superconducting qubits coupled via tunable couplers based on local control theory, an approach commonly employed to steer chemical reactions. Local control theory provides an algorithm that only requires a single forward time propagation of the system wave function to shape an external pulse that monotonically increases the population of a desired final state of a quantum system given an initial state. The method can serve as a starting point for additional refinements that lead to new pulses with improved properties. Among others, we propose an algorithm to design pulses that transfer population in a reversible manner between given initial and final states of coupled fixed-frequency superconducting qubits.

We perform quantum-electrodynamic calculations of the ionization energy of the $1s3d$ states of the ${}^4\mathrm{He}$ atom, including a complete evaluation of the $m{\alpha }^6$ correction. We find a large contribution from the nonradiative part of this correction, which has not been accounted for in previous investigations. The additional contribution shifts theoretical predictions for ionization energies by about $10\sigma$. Despite this shift, we confirm the previously reported systematic deviations between measured experimental results and theoretical predictions for transitions involving $3D$ states. The reason for these deviations remains unknown.