We show how the use of variational states to approximate the ground state of a system can be employed to study a multimode Dicke model. One of the main contributions of this work is the introduction of a not very commonly used quantity, the cooperation number, and the study of its influence on the behavior of the system, paying particular attention to the quantum phase transitions and the accuracy of the used approximations. We also show how these phase transitions affect the dependence of the expectation values of some of the observables relevant to the system and the entropy of entanglement with respect to the energy difference between atomic states and the coupling strength between matter and radiation, thus characterizing the transitions in different ways.

We report experiments on the direct observation of molecular oxygen formation from ${\mathrm{CO}}_2$ in strong laser fields with a reaction microscope. Our accompanying simulations and pump-probe measurements suggest that ${\mathrm{CO}}_2$ molecules undergo bending motion during strong-field ionization which supports the molecular oxygen formation process. The observation of molecular oxygen formation from ${\mathrm{CO}}_2$ may trigger further experimental and theoretical studies on such processes with laser pulses, and provides hints in studies of the ${\mathrm{O}}_2$ and ${\mathrm{O}}_2{}^{+}$ abundance in ${\mathrm{CO}}_2$-dominated planetary atmospheres.

We discuss the problem of finding the best measurement strategy for estimating the value of a quantum system parameter. In general the optimum quantum measurement, in the sense that it maximizes the quantum Fisher information and hence allows one to minimize the estimation error, can only be determined if the value of the parameter is already known. A modification of the quantum Van Trees inequality, which gives a lower bound on the error in the estimation of a random parameter, is proposed. The suggested inequality allows us to assert if a particular quantum measurement, together with an appropriate estimator, is optimal. An adaptive strategy to estimate the value of a parameter, based on our modified inequality, is proposed.

We study compound systems with a classical sector and a quantum sector. Among other consistency conditions we require a canonical structure, that is, a Lie bracket for the dynamical evolution of hybrid observables in the Heisenberg picture, interpolating between the Poisson bracket and the commutator. Weak and strong postulates are proposed. We explicitly construct one such hybrid bracket when the Hilbert space of the quantum sector is finite dimensional and show that it is unique if the strong postulates are enforced. The adjoint bracket for the Schrödinger picture version of the dynamics is also obtained. Unfortunately, preservation of the positivity of the density matrix under the evolution is not guaranteed. The case of a particle with classical position and momentum and quantum spin-$\frac{1}{2}$ is discussed and the spin-orbit dynamics is worked out.

We investigate the transport of energy in a linear chain of two-level quantum emitters (atoms) weakly coupled to a blackbody radiation bath. We show that simply by displacing one or more atoms from their regular-chain positions, the efficiency of the energy transport can be considerably amplified of at least one order of magnitude. In addition, in configurations providing an efficiency greater than $100\%$, the distance between the last two atoms of the chain can be up to 20 times larger than the one in the regular chain, thus achieving a much longer-range energy transport. By performing both a stationary and time-dependent analysis, we ascribe this effect to an elementary block of three atoms, playing the role of excitation injector from the blackbody bath to the extraction site. By considering chains with up to seven atoms, we also show that the amplification is robust and can be further enhanced up to $1400\%$.

We study the faces of the set of quantum correlations, i.e., the Bell and noncontextuality inequalities without any quantum violation. First, we investigate the question of whether every proper (facet-defining) Bell inequality for two parties, other than the trivial ones from positivity, normalization, and no-signaling, can be violated by quantum correlations, i.e., whether the classical Bell polytope or the smaller correlation polytope share any facets with their respective quantum sets. To do this, we develop a recently derived bound on the quantum value of linear games based on the norms of game matrices to give a simple sufficient condition to identify linear games with no quantum advantage. Additionally we show how this bound can be extended to the general class of unique games. We then show that the paradigmatic examples of correlation Bell inequalities with no quantum violation, namely the nonlocal computation games, do not constitute facet-defining Bell inequalities, not even for the correlation polytope. We also extend this to an arbitrary prime number of outcomes for a specific class of these games. We then study the faces in the simplest Clauser-Horne-Shimony-Holt Bell scenario of binary dichotomic measurements, and identify edges in the set of quantum correlations in this scenario. Finally, we relate the noncontextual polytope of single-party correlation inequalities with the cut polytope $\text{CUT}\left(\mathbf{\nabla }G\right)$, where $G$ denotes the compatibility graph of observables in the contextuality scenario and $\mathbf{\nabla }G$ denotes the suspension graph of $G$. We observe that there exist facet-defining noncontextuality inequalities with no quantum violation, and furthermore that this set of inequalities is beyond those implied by the consistent exclusivity principle.

The decoy-state scheme is the most widely implemented quantum-key-distribution protocol in practice. In order to account for the finite-size key effects on the achievable secret key generation rate, a rigorous statistical fluctuation analysis is required. Originally, a heuristic Gaussian-approximation technique was used for this purpose, which, despite its analytical convenience, was not sufficiently rigorous. The fluctuation analysis has recently been made rigorous by using the Chernoff bound. There is a considerable gap, however, between the key-rate bounds obtained from these techniques and that obtained from the Gaussian assumption. Here we develop a tighter bound for the decoy-state method, which yields a smaller failure probability. This improvement results in a higher key rate and increases the maximum distance over which secure key exchange is possible. By optimizing the system parameters, our simulation results show that our method almost closes the gap between the two previously proposed techniques and achieves a performance similar to that of conventional Gaussian approximations.

It is proposed that high-speed universal quantum gates can be realized by using non-Abelian holonomic transformation. A cyclic evolution path which brings the system periodically back to a degenerate qubit subspace is crucial to holonomic quantum computing. The cyclic nature and the resulting gate operations are fully dependent on the precise control of driving parameters, such as the modulated envelop function of Rabi frequency and the control phases. We investigate the effects of fluctuations in these driving parameters on the transformation fidelity of a universal set of single-qubit quantum gates. We compare the damage effects from different noise sources and determine the “sweet spots” in the driving parameter space. The nonadiabatic non-Abelian quantum gate is found to be more susceptible to classical noises on the envelop function than that on the control phases. We also extend our study to a two-qubit quantum gate.

We utilize machine learning models that are based on recurrent neural networks to optimize dynamical decoupling (DD) sequences. Dynamical decoupling is a relatively simple technique for suppressing the errors in quantum memory for certain noise models. In numerical simulations, we show that with minimum use of prior knowledge and starting from random sequences, the models are able to improve over time and eventually output DD sequences with performance better than that of the well known DD families. Furthermore, our algorithm is easy to implement in experiments to find solutions tailored to the specific hardware, as it treats the figure of merit as a black box.

We calculate the two-photon exchange correction to the Lamb shift in muonic ${}^3\mathrm{He}$ ions within the dispersion relations framework. Part of the effort entailed making analytic fits to the electron-${}^3\mathrm{He}$ quasielastic scattering data set, for purposes of doing the dispersion integrals. Our result is that the energy of the $2S$ state is shifted downwards by two-photon exchange effects by 15.14(49) meV, in good accord with the result obtained from a potential model and effective field theory calculation.

We numerically investigate the quantum crystallographic phases of a Rydberg-dressed Bose gas loaded on a square lattice by using the mean-field Gross-Pitaevskii model. For a relatively weak lattice confinement, the phases of ground state undergo amorphism, polycrystal, and polymorphism following the increase of the blockade radius, and if the confinement is stronger, a single crystal with a specific filling factor will be formed. In order to distinctively characterize these phases, the structure function is also studied. In such an anisotropic system, we show that the superfluid-fraction tensor should be a measurable quantity, and an anisotropy parameter can be defined. In addition, for such crystallographic phases, the interaction potential can manifest where the grain boundaries appear.

The experimental realization of two-dimensional (2D) Bose gases with a tunable interaction strength is an important challenge for the study of ultracold quantum matter. Here we report on the realization of an optical accordion creating a lattice potential with a spacing that can be dynamically tuned between 11 and 2 $\mu \mathrm{m}$. We show that we can load ultracold ${}^{87}\mathrm{Rb}$ atoms into a single node of this optical lattice in the large spacing configuration and then decrease nearly adiabatically the spacing to reach a strong harmonic confinement with frequencies larger than ${\omega }_z/2\pi =10$ kHz. Atoms are trapped in an additional flat-bottom in-plane potential that is shaped with a high resolution. By combining these tools we create custom-shaped uniform 2D Bose gases with tunable confinement along the transverse direction and hence with a tunable interaction strength.

A Fermi gas of cold atoms allows precise control over the dimensionless effective range, $k_{\mathrm{F}}{R}_{\mathrm{eff}}$, of the Feshbach resonance. Our pseudopotential formalism allows us to create smooth potentials with effective range, $-2\le k_{\mathrm{F}}{R}_{\mathrm{eff}}\le 2$, which we use for a variational and diffusion Monte Carlo study of the ground state of a unitary Fermi gas. We report values for the universal constants of $\xi =0.388\left(1\right)$ and $\zeta =0.087\left(1\right)$, and compute the condensate fraction, momentum distribution, and pair correlations functions. Finally, we show that a gas with $k_{\mathrm{F}}{R}_{\mathrm{eff}}\gtrsim 1.9$ is thermodynamically unstable.

The spin-asymmetric Josephson effect is a proposed quantum-coherent tunneling phenomenon where Cooper-paired fermionic spin-$\frac{1}{2}$ particles, which are subjected to spin-dependent potentials across a Josephson junction, undergo frequency-synchronized alternating-current Josephson oscillations with spin-dependent amplitudes. Here, in line with present-day techniques in ultracold Fermi gas setups, we consider the regime of small Josephson oscillations and show that the Josephson plasma oscillation amplitude becomes spin dependent in the presence of spin-dependent potentials, while the Josephson plasma frequency is the same for both spin components. Detecting these spin-dependent Josephson plasma oscillations provides a possible means to establish the yet-unobserved spin-asymmetric Josephson effect with ultracold Fermi gases using existing experimental tools.

We theoretically study a strongly driven optomechanical system which consists of a passive optical cavity and an active mechanical resonator. When the optomechanical coupling strength is varied, phase transitions, which are similar to those observed in $\mathcal{PT}$-symmetric systems, are observed. We show that the optical transmission can be controlled by changing the gain of the mechanical resonator and loss of the optical cavity mode. Especially, we find that (i) for balanced gain and loss, optical amplification and absorption can be tuned by changing the optomechanical coupling strength through a control field; (ii) for unbalanced gain and loss, even with a tiny mechanical gain, both optomechanically induced transparency and anomalous dispersion can be observed around a critical point, which exhibits an ultralong group delay. The time delay $\tau$ can be optimized by regulating the optomechanical coupling strength through the control field, and it can be improved up to several orders of magnitude ($\tau \sim 2\mathrm{ms}$) compared to that of conventional optomechanical systems ($\tau \sim 1\mu \mathrm{s}$). The presence of mechanical gain makes the group delay more robust to environmental perturbations. Our proposal provides a powerful platform to control light transport using a $\mathcal{PT}$-symmetric-like optomechanical system.

We analyze theoretically the Schrödinger-Poisson equation in two transverse dimensions in the presence of a Kerr term. The model describes the nonlinear propagation of optical beams in thermo-optical media and can be regarded as an analog system for a self-gravitating self-interacting wave. We compute numerically the family of radially symmetric ground-state bright stationary solutions for focusing and defocusing local nonlinearity, keeping in both cases a focusing nonlocal nonlinearity. We also analyze excited states and oscillations induced by fixing the temperature at the borders of the material. We provide simulations of soliton interactions, drawing analogies with the dynamics of galactic cores in the scalar field dark-matter scenario.

Ultrastrong coupling in circuit quantum electrodynamics makes enhanced fast quantum operations possible. We present a scheme to realize controllable qubit-resonator interactions in ultrastrong circuit quantum electrodynamics with the aid of a unitary transformation. The controllable qubit-resonator interaction is just one type of the so-called selective resonant interactions. From the effective dynamics, it is possible to create the multipartite Dicke states at nanoseconds with high fidelity if the large detuning constraint of the selective resonant interaction is fulfilled. We also investigate the performance of our scheme in the presence of decoherence. Our results present a promising way toward achieving enhanced fast generation of the Dicke states.

We present an intuitive and accurate modal description of the rich optical physics involved for quantum dipole emitters coupled to hybrid plasmonic photonic-cavity structures. A significant frequency dependence for the spontaneous emission decay rate of a quantum dipole emitter coupled to these hybrid structures is found. In particular, it is shown that a Fano-type resonance reported experimentally in hybrid plasmonic systems arises from a large interference between two dominant quasinormal modes of the systems in the frequency range of interest. The presented modal theory forms an efficient basis for modeling quantum light-matter interactions in these complex hybrid systems and also enables the quantitative prediction and understanding of both radiative and nonradiative coupling for a wide range of dipole positions.

Motivated by correlated decay processes producing gain, loss, and lasing in driven semiconductor quantum dots [Phys. Rev. Lett. 113, 036801 (2014); Science 347, 285 (2015); Phys. Rev. Lett. 114, 196802 (2015)], we develop a theoretical technique by using Keldysh diagrammatic perturbation theory to derive a Lindblad master equation that goes beyond the usual second-order perturbation theory. We demonstrate the method on the driven dissipative Rabi model, including terms up to fourth order in the interaction between the qubit and both the resonator and environment. This results in a large class of Lindblad dissipators and associated rates which go beyond the terms that have previously been proposed to describe similar systems. All of the additional terms contribute to the system behavior at the same order of perturbation theory. We then apply these results to analyze the phonon-assisted steady-state gain of a microwave field driving a double quantum dot in a resonator. We show that resonator gain and loss are substantially affected by dephasing-assisted dissipative processes in the quantum-dot system. These additional processes, which go beyond recently proposed polaronic theories, are in good quantitative agreement with experimental observations.