Light-matter interfaces enable the generation of entangled states of light and matter which can be exploited to steer the quantum state of matter through measurement of light and feedback. Here we consider continuous-time, interferometric homodyne measurements of light on an array of light-matter interfaces followed by local feedback acting on each material system individually. While the systems are physically noninteracting, the feedback master equation we derive describes driven-dissipative, interacting many-body quantum dynamics, and comprises pairwise Hamiltonian interactions and collective jump operators. We characterize the general class of driven-dissipative many-body systems which can be engineered in this way, and derive necessary conditions on models supporting nontrivial quantum dynamics beyond what can be generated by local operations and classical communication. We provide specific examples of models which allow for the creation of stationary many-particle entanglement, and the emulation of dissipative Ising models. Since the interaction between the systems is mediated via feedback only, there is no intrinsic limit on the range or geometry of the interaction, making the scheme quite versatile.

The interaction of a quantum system, which is not accessible by direct measurement, with an external probe can be exploited to infer specific features of the system itself. We introduce a probing scheme based on the emergence of spontaneous quantum synchronization between an out-of-equilibrium qubit, in contact with an external environment, and a probe qubit. Tuning the frequency of the probe leads to a transition between synchronization in phase and antiphase. The sharp transition between these two regimes is locally accessible by monitoring the probe dynamics alone and allows one to reconstruct the shape of the spectral density of the environment.

We have measured the ionization fields for Na Rydberg states of $n\ge 26$ by a 79-GHz microwave field. At low $n$, where the microwave frequency $\omega$ is one-third the classical Kepler frequency ${\omega }_K$, which is equal to the $1/n^3$ spacing between $n$ states, the ionization field is $\approx 1/3n^5$, in atomic units. As $n$ is raised ${\omega }_K$ decreases, and the ionization field rises above $1/3n^5$, reaching a constant value when $\omega ={\omega }_K$. At very high $n$, where $\omega >1/2n^2$, single photoionization is possible, and the measured rate agrees with the calculated value. These measurements, together with those done previously, connect the processes of field ionization and photoionization in Na. At low $n$ and radio frequencies ionization is simply field ionization, and at very high $n$ it occurs by photoionization, single-photon absorption. These measurements also show that microwave ionization of Rydberg atoms at 79 GHz results in significant populations' being left in the very high-lying states.

We theoretically reveal the potential of the parallelism of squeezed state generation by nonlinear pulse propagation in an optical fiber. Starting from a nonlinear Schrödinger equation coupling with phonon modes that cause Raman noise, we develop a multimode quantum theory of nonlinear propagation in an optical fiber. Based on our proposed method, we numerically simulate fiber nonlinear propagation in two conditions: solitonlike and zero-group-delay-dispersion (zero-GVD) propagation. As a result, we find that zero-GVD propagation enables the large-scale parallel generation of squeezed states relative to solitonlike propagation owing to the broadband phase matching of the four-wave mixing process.

We studied the critical dynamics of spectral singularities. The system investigated is a coupled resonator array with a side-coupled loss (gain) resonator. For a gain resonator, the system acts as a wave emitter at spectral singularities. The reflection probability increased linearly over time. The rate of increase is proportional to the width of the incident wave packet, which served as the spectral singularity observer in the experiment. For a lossy resonator, the system acts as a wave absorber. The emission and absorption states at spectral singularities coalesce in a finite parity-time $\left(\mathcal{PT}\right)$ symmetric system that combined by the gain and loss structures cut from corrresponding scattering systems at spectral singularities; in this case, the $\mathcal{PT}$-symmetric system is at an exceptional point with a $2\times 2$ Jordan block. The dynamics of the $\mathcal{PT}$-symmetric system exhibit the characteristic of exceptional points and spectral singularities.

We theoretically analyze the cooling dynamics of a high-Q mode of a mechanical resonator, when the structure is also an optical cavity and is coupled with a nitrogen-vacancy (NV) center. The NV center is driven by a laser and interacts with the cavity photon field and with the strain field of the mechanical oscillator, while radiation pressure couples the mechanical resonator and cavity field. Starting from the full master equation we derive the rate equation for the mechanical resonator's motion, whose coefficients depend on the system parameters and on the noise sources. We then determine the cooling regime, the cooling rate, the asymptotic temperatures, and the spectrum of resonance fluorescence for experimentally relevant parameter regimes. For these parameters, we consider an electronic transition, whose linewidth allows one to perform sideband cooling, and show that the addition of an optical cavity in general does not improve the cooling efficiency. We further show that pure dephasing of the NV center's electronic transitions can lead to an improvement of the cooling efficiency.

We present an observation of the rotational Doppler shift in the frequency of optical harmonic generated in fast rotating molecules. Conservation of energy and angular momentum in the light-molecule interaction suggests four different kinds of shifts depending on the mutual handedness of the circularly polarized fundamental and harmonic fields, as well as the handedness of the molecular rotation. All four types of the frequency shifts were observed in our experiments on third-harmonic generation in a gas of fast spinning ${\mathrm{O}}_2$ molecules.

Quantum metrology with entangled states in realistic noisy environments always suffers from decoherence. Therefore, the measurement precision is greatly reduced. Here we applied the dynamical decoupling method to protect the $N$-qubit quantum metrology protocol and successfully revived the scaling of the measurement precision as $N^{-k}$ with $k\in \left[5/6,11/12\right]$. The degree of the precision revival, as determined by the noise spectrum distribution, indicates that the performance of the protected protocol can be further improved by controlling the noise spectrum. Such a protected protocol is proved to be universal for entanglement-based quantum metrology in the pure dephasing and relaxation noise, which should stimulate the development of practical quantum metrology for weak signal detection of microscopic physics.

We have been investigating the problem of the Anderson localization in a disordered one-dimensional tight-binding model. The disorder is created by the interaction of mobile particles with other species, immobilized at random positions. We introduce a method of creating correlations in the optical lattices with such a kind of disorder by using two different lattices with commensurate lattice lengths to hold two species of the particles. Such a model, called the generalized random $N$-mer model, leads to the appearance of multiple extended states in contrast to a localization of all states usually expected in one dimension. We develop a method, based on properties of transfer matrices which can be used to determine the presence of extended states and their energies for that class of correlations. Analytical results are compared with the numerical calculations for several cases which can be realized in cold-atom experiments.

A universal $k^{-4}$ decay of the large-momentum tails of the momentum distribution, fixed by Tan's contact coefficients, constitutes a direct signature of strong correlations in a short-range interacting quantum gas. Here we consider a repulsive multicomponent Fermi gas under harmonic confinement, as in the experiment of G. Pagano et al. [Nat. Phys. 10, 198 (2014)], realizing a gas with tunable $\text{SU}\left(\kappa \right)$ symmetry. We exploit an exact solution at infinite repulsion to show a direct correspondence between the value of the Tan's contact for each of the $\kappa$ components of the gas and the Young tableaux for the $S_N$ permutation symmetry group identifying the magnetic structure of the ground state. This opens a route for the experimental determination of magnetic configurations in cold atomic gases, employing only standard (spin-resolved) time-of-flight techniques. Combining the exact result with matrix-product-state simulations, we obtain the Tan's contact at all values of repulsive interactions. We show that a local-density approximation (LDA) on the Bethe-ansatz equation of state for the homogeneous mixture is in excellent agreement with the results for the harmonically confined gas. At strong interactions, the LDA predicts a scaling behavior of the Tan's contact. This provides a useful analytical expression for the dependence on the number of fermions, number of components, and interaction strength. Moreover, using a virial approach, we study the Tan's contact behavior at high temperature and in the limit of infinite interactions, and we show that it increases with the temperature and the number of components. At zero temperature, we predict that the weight of the momentum distribution tails increases with interaction strength and the number of components if the population per component is kept constant. This latter property was experimentally observed in G. Pagano et al. [Nat. Phys. 10, 198 (2014)].

Recent realizations of quantum gas microscopy offer the possibility of continuous monitoring of the dynamics of a quantum many-body system at the single-particle level. By analyzing effective non-Hermitian Hamiltonians for interacting bosons in an optical lattice and continuum, we demonstrate that the backaction of quantum measurement shifts the quantum critical point and gives rise to a unique critical phase beyond the terrain of the standard universality class. We perform mean-field and strong-coupling-expansion analyses and show that non-Hermitian contributions shift the superfluid–Mott-insulator transition point. Using a low-energy effective field theory, we discuss critical behavior of the one-dimensional interacting Bose gas subject to the measurement backaction. We derive an exact ground state of the effective non-Hermitian Hamiltonian and find a unique critical behavior beyond the Tomonaga-Luttinger liquid universality class. We propose experimental implementations of postselections using a quantum gas microscope to simulate the non-Hermitian dynamics and argue that our results can be investigated with current experimental techniques in ultracold atoms.

We propose to couple single atomic qubits to photons incident on a cavity containing an atomic ensemble of a different species that mediates the coupling via Rydberg interactions. Subject to a classical field and the cavity field, the ensemble forms a collective dark state which is resonant with the input photon, while excitation of a qubit atom leads to a secondary “dark” state that splits the cavity resonance. The two different dark-state mechanisms yield zero and $\pi$ reflection phase shifts and can be used to implement quantum gates between atomic and optical qubits.

We search for mirror and cavitylike features of a linear chain of atoms in which one of the atoms is specially chosen as a probe atom that is initially prepared in its excited state or is continuously driven by a laser field. Short chains are considered, composed of only three and five atoms. The analysis demonstrates the importance of the interatomic dipole-dipole interaction, which may lead to a collective ordering of the emission along some specific directions. We examine the conditions under which the radiative modes available for the emission are only those contained inside a cone centered about the interatomic axis. Particular interest is in achieving one-way emission along the interatomic axis, in either the left (backward) or the right (forward) direction, which is referred to as a mirrorlike behavior of the atomic chain. A direction-dependent quantity called the directivity function, which determines how effective the system is in concentrating the radiation in a given direction, is introduced. We show that the function depends crucially on the distance between the atoms and find that there is a threshold for the interatomic distances above which a strongly directional emission can be achieved. The one-sided emission as a manifestation of the mirrorlike behavior and a highly focused emission along the interatomic axis as a characteristic of a single-mode cavity are demonstrated to occur in the stationary field. Below the threshold the directivity function is spherically symmetric. However, we find that the population can be trapped in one of the atoms, and sometimes in all atoms, indicating that at these short distances the system decays to a state for which there are no radiative modes available for emission.

We investigate the nonlinear optical susceptibility of an alkali-metal atom with tripod electronic configuration responsible for generating cross-phase modulation and self-phase modulation under the condition of double-double electromagnetically induced transparency. Our investigation demonstrates an enhancement in the nonlinear optical susceptibility of an alkali-metal atom by a factor of 1000 in the region of the second transparency window. This enhancement is in comparison with the atom's susceptibility in the first transparency window for the same parameters under the same conditions. Nonlinear-absorption enhancement arises by canceling Raman-gain generation, which arises when the probe and signal fields have equal intensities. At the center of the second transparency window, we obtain the condition required to attain a nonvanishing nonlinear optical susceptibility. In the bare-state picture, the coupling field must be off resonant from a bare-to-bare-state transition, while working in the semiclassical dressed picture required the signal field to be tuned off resonantly with a bare-to-dressed-state transition. The relation that governs the values of coupling- and signal-field detuning are also obtained. Our scheme exhibits the fact that the second transparency window has advantages over the first transparency window with respect to obtaining an enhanced Kerr effect, and our calculation includes simulation of both low-temperature and Doppler-broadened regimes.

The force estimation problem in quantum metrology with an arbitrary non-Markovian Gaussian bath is considered. No assumptions are made on the bath spectrum and coupling strength with the probe. Considering the natural global unitary evolution of both bath and probe and assuming initial global Gaussian states, we are able to solve the main issues of any quantum metrological problem: the best achievable precision determined by the quantum Fisher information, the best initial state, and the best measurement. Studying the short-time behavior and comparing with regular Markovian dynamics we observe an increase in quantum Fisher information. We emphasize that this phenomenon is due to the ability to perform measurements below the correlation time of the bath, activating non-Markovian effects. This brings huge consequences for the sequential preparation-and-measurement scenario because the quantum Fisher information becomes unbounded when the initial probe mean energy goes to infinity, whereas its Markovian counterpart remains bounded by a constant. The long-time behavior shows the complexity and potential variety of non-Markovian effects, somewhere between the exponential decay characteristic of Markovian dynamics and the sinusoidal oscillations characteristic of resonant narrow bands.

We apply the method of direct perturbation theory for the Foldy-Wouthuysen (FW) transformation upon the Dirac-Pauli Hamiltonian subject to external electromagnetic fields. The exact FW transformations exist and agree with those obtained by Eriksen's method for two special cases. In the weak-field limit of static and homogeneous electromagnetic fields, by mathematical induction on the orders of $1/c$ in the power series, we rigorously prove the long-held speculation: the FW transformed Dirac-Pauli Hamiltonian is in full agreement with the classical counterpart, which is the sum of the orbital Hamiltonian for the Lorentz force equation and the spin Hamiltonian for the Thomas-Bargmann-Michel-Telegdi equation.

We critically evaluate the most widespread assumption in the theoretical description of coherent control strategies for open quantum systems. We show that, for non-Markovian open systems dynamics, this fixed-dissipator assumption leads to a serious pitfall generally causing difficulties in the effective modeling of the controlled system. We show that at present, to avoid these problems, a full microscopic description of the controlled system in the presence of noise may often be necessary. We illustrate our findings with a paradigmatic example.

We show the emergence of spontaneous synchronization between a pair of detuned quantum oscillators within a harmonic network. Our model does not involve any nonlinearity, driving, or external dissipation, thus providing the simplest scenario for the occurrence of local coherent dynamics in an extended harmonic system. A sufficient condition for synchronization is established by building upon the Rayleigh normal mode approach to vibrational systems. Our results show that mechanisms favoring synchronization, even between oscillators that are not directly coupled to each other, are transient energy depletion and crosstalk. We also address the possible buildup of quantum correlations during synchronization and show that indeed entanglement may be generated in detuned systems, starting from uncorrelated states and without any direct coupling between the two oscillators.