A ring of dipole-coupled quantum emitters positioned at subwavelength distances possesses only a few radiant but many subradiant collective excitations with lifetimes growing exponentially with the atom number. These exhibit a three-dimensionally confined spatial radiation field pattern and form nanoscale high-$Q$ optical resonators. Tailoring size, orientation, and distance between two rings allows for increasing the ratio of coherent ring-to-ring energy transfer versus free-space emission by orders of magnitude. In particular, the more dark and delocalized over several sites are excitons, the higher is their fidelity for transport to a second ring.

We propose a scheme to simultaneously cool two mechanical oscillators in a dissipatively coupled optomechanical system. Calculating the mean phonon numbers of the two mechanical oscillators in steady state, we find that there are two cooling regions. Both mechanical oscillators can be cooled efficiently in the two cooling regions. We also find that when the coupling strength between the two mechanical oscillators is large, the second mechanical oscillator can be cooled to a temperature lower than the first mechanical oscillator. This feature can be understood as the entanglement between two phononic supermodes of the two mechanical oscillators. When the coupling strength is small, the second mechanical oscillator can also be cooled, but cannot reach a temperature lower than the first mechanical oscillator, as the thermal fluctuations of reservoir cannot be ignored. The quantum cooling limits of the two mechanical oscillators are discussed for both the strong and weak couplings between the two mechanical oscillators.

The trace distance between two quantum states, $\rho$ and $\sigma$, is an operationally meaningful quantity in quantum information theory. However, in general it is difficult to compute, involving the diagonalization of $\rho -\sigma$. In contrast, the Hilbert-Schmidt distance can be computed without diagonalization, although it is less operationally significant. Here, we relate the trace distance and the Hilbert-Schmidt distance with a bound that is particularly strong when either $\rho$ or $\sigma$ is low rank. Our bound is stronger than the bound one could obtain via the norm equivalence of the Frobenius and trace norms. We also consider bounds that are useful not only for low-rank states but also for low-entropy states. Our results have relevance to quantum information theory, quantum algorithm design, and quantum complexity theory.

The debate instigated by the seminal works of Einstein, Podolsky, Rosen, and Bell put the notions of realism and nonlocality at the core of almost all philosophical and physical discussions underlying the foundations of quantum mechanics. However, while experimental criteria and quantifiers are by now well established for nonlocality, there is no clear quantitative measure for the degree of reality associated with continuous variables such as position and momentum. This work aims at filling this gap. Considering position and momentum as effectively discrete observables, we implement an operational notion of projective measurement and, from that, a criterion of reality for theses quantities. Then we introduce a quantifier for the degree of irreality of a discretized continuous variable which, when applied to the conjugated pair position-momentum, is shown to obey an uncertainty relation, meaning that quantum mechanics prevents classical realism for conjugated quantities. As an application of our formalism, we study the emergence of elements of reality in an instance where a Gaussian state is submitted to the dissipative dynamics implied by the Caldirola-Kanai Hamiltonian. In particular, at equilibrium, we make some links with the measurement problem and identify aspects that can be taken as the quantum counterpart for the notion of rest.

High-precision manipulation of multiqubit quantum systems requires strictly clocked and synchronized multichannel control signals. However, practical arbitrary wave-form generators always suffer from random signal jitters and channel latencies that induce nonignorable state or gate operation errors. In this paper, we analyze the average gate error caused by clock noises, from which an estimation formula is derived for quantifying the control robustness against clock noises. This measure is then employed for finding robust controls via a homotopic optimization algorithm. We also introduce our recently proposed stochastic optimization algorithm, b-grape, for training robust controls via randomly generated clock-noise samples. Numerical simulations on a two-qubit example demonstrate that both algorithms can greatly improve the control robustness against clock noises. The homotopic algorithm converges much faster than the b-grape algorithm, but the latter can achieve higher control robustness.

We consider identical quantum bosons with weak contact interactions in a two-dimensional isotropic harmonic trap. When the interactions are turned off, the energy levels are equidistant and highly degenerate. At linear order in the coupling parameter, these degenerate levels split, and we study the patterns of this splitting. It turns out that the problem is mathematically identical to diagonalizing the quantum resonant system of the two-dimensional Gross-Pitaevskii equation, whose classical counterpart has been studied previously in the mathematical literature on turbulence. Our purpose is to explore the implications of the symmetries and energy bounds of this resonant system, previously studied for the classical case, for the quantum level splitting. Simplifications in computing the splitting spectrum numerically result from exploiting the symmetries. The highest energy state emanating from each unperturbed level is explicitly described by our analytics. We furthermore discuss the energy-level spacing distributions in the spirit of quantum chaos theory. After separating the eigenvalues into blocks with respect to the known conservation laws, we observe the Wigner-Dyson statistics within specific large blocks, which leaves little room for further integrable structures in the problem beyond the symmetries that are already explicitly known.

We experimentally investigate a weakly disordered one-dimensional Anderson-localizing lasing system in the neighborhood of the critical disorder. This critical disorder ${\delta }_{\text{cr}}$ separates two regimes, in one of which the transport parameters show a wavelength dependence, but not in the other. We first theoretically study the temporal characteristics of lasing pulses, and extract the lifetimes of the lasing modes. The distribution of the lifetimes shows a bimodal distribution under the ${\delta }_{\text{cr}}$, which condenses into a monomodal distribution beyond the ${\delta }_{\text{cr}}$. Next, we implement an experimental scheme using a linear array of microresonators with gain, which sustains Anderson localization. Emission pulses were analyzed on a streak camera to build lifetime distributions in the experimental samples, which reproduced the theoretical predictions to a very good degree. These observations provide a direct demonstration of the effect of critical disorder on Anderson-localizing lasing systems.

Static synthetic magnetic fields give rise to phenomena including the Lorentz force and the quantum Hall effect even for neutral particles, and they have by now been implemented in a variety of physical systems. Moving toward fully dynamical synthetic gauge fields allows, in addition, for backaction of the particles' motion onto the field. If this results in a time-dependent vector potential, conventional electromagnetism predicts the generation of an electric field. Here, we show how synthetic electric fields for photons arise self-consistently due to the nonlinear dynamics in a driven system. Our analysis is based on optomechanical arrays, where dynamical gauge fields arise naturally from phonon-assisted photon tunneling. We study open, one-dimensional arrays, where synthetic magnetic fields are absent. However, we show that synthetic electric fields can be generated dynamically. The generation of these fields depends on the direction of photon propagation, leading to a mechanism for a photon diode, inducing nonlinear unidirectional transport via dynamical synthetic gauge fields.

Using the example of the Jaynes-Cummings model, we present a comparison between time-delayed coherent feedback mediated by reservoirs with continuous- and discrete-mode structures and work out their qualitative differences. In contrast to the discrete-mode case, the continuous-mode case results in the well-known single-delay dynamics which can, e.g., stabilize Rabi oscillations. The discrete-mode case, however, shows population trapping, not present in the continuous-mode model. Given these differences, we discuss the cavity output spectra and show how these characteristic properties are spectrally identifiable. This work demonstrates the fundamental difference between the continuous-mode case, which represents a truly dissipative mechanism, and the discrete-mode case that is in principle based on a coherent excitation exchange process.

We consider a protocol for sharing quantum states using continuous variable systems. Specifically we introduce an encoding procedure where bosonic modes in arbitrary secret states are mixed with several ancillary squeezed modes through a passive interferometer. We derive simple conditions on the interferometer for this encoding to define a secret sharing protocol and we prove that they are satisfied by almost any interferometer. This implies that, if the interferometer is chosen uniformly at random, the probability that it may not be used to implement a quantum secret sharing protocol is zero. Furthermore, we show that the decoding operation can be obtained and implemented efficiently with a Gaussian unitary using a number of single-mode squeezers that is at most twice the number of modes of the secret, regardless of the number of players. We benchmark the quality of the reconstructed state by computing the fidelity with the secret state as a function of the input squeezing.

We present above-threshold ionization (ATI) in the molecule nitric oxide, NO, by intense (${10}^{12}–{10}^{13}\mathrm{W}/{\mathrm{cm}}^2$) two-color femtosecond laser pulses. Vibrationally resolved coherent interference phenomena of multiphoton and multipathway ionization processes have been investigated by measuring experimentally and modeling theoretically the molecular photoionization yields. We find that the ATI photoelectron distribution of NO, initiated from degenerate electronic and vibrational states, depends on the relative phase of the two pulses, the kinetic energy, and emission angle of the photoelectrons. This dependence codes the information of interference effects of molecular electronic states. AC Stark effects modulate interference patterns in ATI spectra. Moreover, the ATI spectra exhibit peak energy dependencies that illustrate interference effects from coherent couplings between various ionization channels. These features reflect the molecular property and the multiple channel ionization interference effects in ATI processes. The results allow to explore coherent electron-vibration processes in ultrafast molecular photoionization.

We study the momentum distributions and spatial correlations of few harmonically confined SU($N$) fermions using quantum Monte Carlo methods. In our study, we vary the spin degeneracy $N$ from 2 to 6 and the total number of particles from 6 to 18. Only balanced mixtures, with the same number of atoms per spin type, and repulsive unlike-spin contact interactions are considered. Going from $N=2$ to $N=6$, with the same occupancy of each spin state, we observe an increase of atom-atom correlations. This effect is particularly significant in the momentum distributions, which show fatter tails at large $k$ ($k\sigma >5, \sigma$ being the oscillator length) when $N$ grows, in agreement with experimental findings. Those tails also show the expected $k^{-4}$ decay related to the Tan contact for different values of the spin degeneracy. According to our results, the local spin ordering and the spin-spin correlations are mainly determined by $N$ via the Pauli exclusion principle, with minor influences from the particle-particle interactions, irrespective of the total number of confined atoms.

While the manipulation of quantum systems has been significantly developed, achieving a single-source multiuse system for quantum-information processing and networks is still challenging. A virtual state, a so-called dressed state, is a potential host for quantum hybridizations of quantum physical systems with various operational ranges. We present an experimental demonstration of a dressed state generated by two-photon magnetic resonances using a single spin in a single nitrogen-vacancy center in diamond. The two-photon magnetic resonances occur under the application of microwave and radio-frequency fields, with different operational ranges. The experimental results reveal the behavior of two-photon magnetic transitions in a single defect spin in a solid, thus presenting potential quantum and semiclassical hybrid systems with different operational ranges using superconductivity and spintronics devices.

We study theoretically the statistics of photons generated by a quantum emitter located in the vicinity of a periodic plasmonic nanostructure. The presented formalism is based on a macroscopic QED formalism in conjunction with a density-matrix approach in order to obtain the second-order correlation function of the emitted photons accounting for the influence of the plasmonic environment. The metallic reservoir coupling is computed using Green's-function theory, which, for a periodic lattice of scatterers, is calculated by a multiple-scattering method. We show that the photon statistics and the antibunching of emitted photons depend very strongly on the orientation of the quantum emitter relative to the lattice, on the transition frequency of the emitter, on the intensity of the applied field, and on the geometrical parameters of the nanoparticles, such as the shell thickness.

The evolution of quantum light through linear optical devices can be described by the scattering matrix $S$ of the system. For linear optical systems with $m$ possible modes, the evolution of $n$ input photons is given by a unitary matrix $U={\phi }_{m,M}\left(S\right)$, derived from a known homomorphism, ${\phi }_{m,M}$, which depends on the size of the resulting Hilbert space of the possible photon states, $M$. We present a method to decide whether a given unitary evolution $U$ for $n$ photons in $m$ modes can be achieved with linear optics or not and the inverse transformation ${\phi }_{m,M}^{-1}$ when the transformation can be implemented. Together with previous results, the method can be used to find a simple optical system which implements any quantum operation within the reach of linear optics. The results come from studying the adjoint map between the Lie algebras corresponding to the Lie groups of the relevant unitary matrices.

We have investigated the structural dynamics in photoexcited 1,2-diiodotetrafluoroethane molecules $\left({\mathrm{C}}_2{\mathrm{F}}_4{\mathrm{I}}_2\right)$ in the gas phase experimentally using ultrafast electron diffraction and theoretically using FOMO-CASCI excited-state dynamics simulations. The molecules are excited by an ultraviolet femtosecond laser pulse to a state characterized by a transition from the iodine $5p\perp$ orbital to a mixed $5p\parallel \sigma$ hole and ${\mathrm{CF}}_2^{•}$ antibonding orbital, which results in the cleavage of one of the carbon-iodine bonds. We have observed, with sub-Angstrom resolution, the motion of the nuclear wave packet of the dissociating iodine atom followed by coherent vibrations in the electronic ground state of the ${\mathrm{C}}_2{\mathrm{F}}_4\mathrm{I}$ radical. The radical reaches a stable classical (nonbridged) structure in less than 200 fs.

We extend the recently developed technique of opto-optical modulation (OOM) to probe state-resolved ac-Stark-induced phase variations of a coherently excited ensemble of helium atoms. In a joint experimental and theoretical study, we find that the spatial redirection of the resonant emission from the OOM process is different for the low-lying $1s2p$ state as compared with the higher-lying Rydberg states, and that this redirection can be controlled through the spatial characteristics of the infrared (IR) probe beam. In particular, we observe that the intensity dependence of the IR-induced Stark phase on the $1s2p$ emission is nonlinear, and that the phase accumulation changes sign for moderate intensities. Our results suggest that OOM, combined with precise experimental shaping of the probe beam, could allow future measurements of Stark-induced phase shifts of excited states.

In this article we study the quench dynamics of Galilean and scale-invariant many-body systems which can be prepared using interacting atomic gases. The far-from-equilibrium dynamics is investigated by employing $m$-body density matrices, which are most conveniently defined in terms of a special basis, the conformal tower states. We explicitly illustrate that, although during the initial stage of the dynamics all symmetries can be broken and absent in the unitary evolution because of the initialization of the state, there is always an emergent conformal symmetry in the long-time limit. The emergence of this dynamic conformal symmetry is robust and always occurs, even when scale and other symmetries (such as rotational symmetry) are still fully broken in the many-body states; it uniquely defines the characteristics of the asymptotic dynamics near a scale-invariant strong-coupling fixed point. As an immediate application of the asymptotic dynamics of the microscopic density matrices, we focus on the effects of this emergent conformal symmetry on two observables: the moment of inertia tensor $I_{ij}\left(t\right), i,j=x,y,z$, and the entropy density field $S(\mathbf{r},t)$ in the hydrodynamic flow of strongly interacting particles. We show that the long-time behavior of these observables is completely set by conformal symmetry, while the leading long-time corrections depend on interference effects between different conformal tower states. The emergent conformal symmetry naturally leads to entropy conservation and conformal cooling, an energy-conserving cooling of a strongly interacting gas during free expansion. When the interaction Hamiltonian breaks the scale symmetry, we further demonstrate that there is a direct cause-effect relation between conformal symmetry breaking in the long-time limit and a nonvanishing entropy production. This suggests that the entropy production rate is a natural parameter for categorizing the breaking of conformal symmetry.