We use the exact calculation of the quantum mechanical, temporal characteristic function $\chi \left(\eta \right)$ and the degree of second-order coherence $g^{\left(2\right)}\left(\tau \right)$ for a single-mode, degenerate parametric amplifier for a system in the Gaussian state, viz., a displaced-squeezed thermal state, to study the different criteria for nonclassicality. In particular, we contrast criteria that involve only one-time functions of the dynamical system, for instance, the quasiprobability distribution $P\left(\beta \right)$ of the Glauber-Sudarshan coherent or P representation of the density of state and the Mandel $Q_M\left(\tau \right)$ parameter, versus the criteria associated with the two-time correlation function $g^{\left(2\right)}\left(\tau \right)$.

Particles of low velocity, traveling without dissipation in a superfluid, can interact and emit sound when they collide. We propose a minimal model in which the equations of motion of the particles, including a short-range repulsive force, are self-consistently coupled with the Gross-Pitaevskii equation. We show that this model generates naturally an effective superfluid-mediated attractive interaction between the particles; and we study numerically the collisional dynamics of particles as a function of their incident kinetic energy and the length scale of the repulsive force. We find a transition from almost elastic to completely inelastic (sticking) collisions as the parameters are tuned. We find that aggregation and clustering result from this sticking transition in multiparticle systems.

The information content of the two-particle one- and two-dimensional Calogero model is studied by using the von Neumann and Rényi entropies. The one-dimensional model is shown to have nonmonotonic entropies with finite values in the large-interaction-strength limit. On the other hand, the von Neumann entropy of the two-dimensional model with isotropic confinement is a monotone increasing function of the interaction strength which diverges logarithmically. By considering an anisotropic confinement in the two-dimensional case we show that the one-dimensional behavior is eventually reached when the anisotropy increases. The crossover from two to one dimensions is demonstrated by using the harmonic approximation and it is shown that the von Neumann divergence only occurs in the isotropic case. The Rényi entropies are used to highlight the structure of the model spectrum. In particular, it is shown that these entropies have a nonmonotonic and nonanalytical behavior in the neighborhood of the interaction strength parameter values where the Hilbert space and, consequently, the spectrum of the reduced density matrix are both finite.

The quantum character of Josephson junctions is ordinarily revealed through the analysis of the switching currents, i.e., the current at which a finite voltage appears: A sharp rise of the voltage signals the passage (tunnel) from a trapped state (the zero voltage solution) to a running state (the finite voltage solution). In this context, we investigate the probability distribution of the Josephson-junction switching current taking into account the effect of the bias sweeping rate and introducing a simple nonideal quantum measurement scheme. The measurements are modeled as repeated voltage samplings at discrete time intervals, that is, with repeated projections of the time-dependent quantum solutions on the static or the running states, to retrieve the probability distribution of the switching currents. The distribution appears to be immune to the quantum Zeno effect, and it is close to, but distinguishable from, the Wentzel-Kramers-Brillouin approximation. For energy barriers comparable to the quantum fundamental energy state and in the fast bias current ramp rate the difference is neat, and remains sizable in the asymptotic slow rate limit. This behavior is a consequence of the quantum character of the system that confirms the presence of a backreaction of quantum measurements on the outcome of mesoscopic Josephson junctions.

It is shown how possible corrections to ordinary quantum mechanics described by the Lindblad equation might be detected by exploiting the great precision of atomic clocks.

The ground-state properties of a few spin-1/2 fermions with different masses and interacting via short-range contact forces are studied within an exact diagonalization approach. It is shown that, depending on the shape of the external confinement, different scenarios of the spatial separation between components manifested by specific shapes of the density profiles can be obtained in the strong interaction limit. We find that the ground-state of the system undergoes a specific transition between orderings when the confinement is changed adiabatically from a uniform box to a harmonic oscillator shape. We study the properties of this transition in the framework of the finite-size scaling method adopted to few-body systems.

We construct Einstein-Podolsky-Rosen (EPR) steering signatures for the nonlocality of the entangled superposition state described by $\frac{1}{\sqrt{2}}\left\{\right|N\rangle |0\rangle +|0\rangle |N\rangle \}$, called the two-mode NOON state. The signatures are a violation of an EPR steering inequality based on an uncertainty relation. The violation confirms an EPR steering between the two modes and involves certification of an intermode correlation for number, as well as quadrature phase amplitude measurements. We also explain how the signatures certify an $N\mathrm{th}$ order quantum coherence, so the system (for larger $N$) can be signified to be in a superposition of states distinct by a mesoscopic value of quantum number in each mode. Finally, we examine the limitations imposed for lossy scenarios, discussing how experimental realizations may be possible for $N=2,3$.

We describe an experimental implementation to generate and measure high-dimensional time-bin-entangled qudits. Two-photon time-bin entanglement is generated via spontaneous four-wave mixing in single-mode fiber. Unbalanced Mach-Zehnder interferometers transform selected time bins to polarization entanglement, allowing standard polarization-projective measurements to be used for complete quantum state tomographic reconstruction. Here we generate maximally entangled qubits $(d=2)$, qutrits $(d=3)$, and ququarts $(d=4)$, as well as other phase-modulated nonmaximally entangled qubits and qutrits. We reconstruct and verify all generated states using maximum-likelihood estimation tomography.

We simulate nuclear and electron spin relaxation rates in a paramagnetic system from first principles. Sampling a molecular dynamics trajectory with quantum-chemical calculations produces a time series of the instantaneous parameters of the relevant spin Hamiltonian. The Hamiltonians are, in turn, used to numerically solve the Liouville–von Neumann equation for the time evolution of the spin density matrix. We demonstrate the approach by studying the aqueous solution of the ${\mathrm{Ni}}^{2+}$ ion. Taking advantage of Kubo's theory, the spin-lattice $\left(T_1\right)$ and spin-spin $\left(T_2\right)$ relaxation rates are extracted from the simulations of the time dependence of the longitudinal and transverse magnetization, respectively. Good agreement with the available experimental data is obtained by the method.

We consider a spin-1 Bose-Einstein condensate with Rashba spin-orbit coupling and dipole-dipole interaction confined in a cigar-shaped trap. Due to the combined effects of spin-orbit coupling, dipole-dipole interaction, and trap geometry, the system exhibits a rich variety of ground-state spin structures, including twisted spin vortices. The ground-state phase diagram is determined with respect to the strengths of the spin-orbit coupling and dipole-dipole interaction.

Coherent coupling generated by laser light between the hyperfine states of atoms, loaded in a one-dimensional (1D) optical lattice, gives rise to the “synthetic dimension” system which is equivalent to a Hofstadter model in a finite strip of square lattice. An SU($M$) symmetric attractive interaction in conjunction with the synthetic gauge field present in this system gives rise to unusual effects. We study the two-body problem of the system using the $T$-matrix formalism. We show that the two-body ground states pick up a finite momentum and can transform into two-body resonancelike features in the scattering continuum with a large change in the phase shift. As a result, even for this 1D system, a critical amount of attraction is needed to form bound states. These phenomena have spectacular effects on the many-body physics of the system analyzed using the numerical density matrix renormalization group technique. We show that the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states form in the system even for a “balanced” gas and the FFLO momentum of the pairs scales linearly with flux. Considering suitable measures, we investigate interesting properties of these states. We also discuss a possibility of realization of a generalized interesting topological model, called the Creutz ladder.

We study the effect of an external harmonic trapping potential on an outcome of the nonadiabatic quantum phase transition from an antiferromagnetic to a phase-separated state in a spin-1 atomic condensate. Previously, we demonstrated that the dynamics of an untrapped system exhibits double universality with two different scaling laws appearing due to the conservation of magnetization. We show that in the presence of a trap, double universality persists. However, the corresponding scaling exponents are strongly modified by the transfer of local magnetization across the system. The values of these exponents cannot be explained by the effect of causality alone, as in the spinless case. We derive the appropriate scaling laws based on a slow diffusive-drift relaxation process in the local density approximation.

We show the renormalization of the contact interaction for odd-wave scattering in one-dimension (1D). Based on the renormalized interaction, we exactly solve the two-body problem in a harmonic trap and further explore the universal properties of spin-polarized fermions near odd-wave resonance by using the operator-product-expansion method. It is found that the high-momentum distribution behaves as $C/k^2$, with $C$ being the odd-wave contact. Various universal relations are derived. Our work suggests a universal system emergent in 1D with large odd-wave scattering length.

We study the statistics of the fluorescence decay rates for single quantum emitters embedded in a scattering medium undergoing a phase transition. Under certain circumstances, the structural properties of the scattering medium explore a regime in which the system dynamically switches between two different phases. While in that regime the light-scattering properties of both phases are hardly distinguishable, we demonstrate that the lifetime statistics of single emitters with low diffusivity is clearly dependent on the dynamical state in which the medium evolves. Hence, lifetime statistics provides clear signatures of phase switching in systems where light scattering does not.

The recent advent of wave-shaping methods has demonstrated the focusing of light through and inside even the most strongly scattering materials. Typically in wavefront shaping, light is focused in an area with the size of one speckle spot. It has been shown that the intensity is not only increased in the target speckle spot, but also in an area outside the optimized speckle spot. Consequently, the total transmission is enhanced, even though only the intensity in a single speckle spot is controlled. Here, we experimentally study how the intensity enhancement on both interfaces of a scattering medium depends on the optimization area on the transmission side. We observe that as the optimization radius increases, the enhancement of the total transmitted intensity increases. We find a concomitant decrease of the total reflected intensity, which implies an energy redistribution between transmission and reflection channels. In addition, we find qualitative evidence of a long-range reflection-transmission correlation. Our result is useful for efficient light harvesting in solar cells, multichannel quantum secure communications, imaging, and complex beam delivery through a scattering medium.

Photonic crystal fibers doped with silver nanoparticles exhibit a Kerr nonlinearity that can be positive or negative depending on the input wavelength and which vanishes at a specific wavelength. The existence of negative nonlinearity allows soliton formation even in the normal-dispersion region of the fiber, and the zero-nonlinearity wavelength (ZNW) acts as a barrier for the Raman-induced redshift of solitons. We adopted the variational principle to understand the role of the zero-nonlinearity point on Raman redshift and verified its prediction numerically for fundamental and higher-order solitons. We show how the simultaneous presence of a ZNW and a zero-dispersion wavelength affects soliton evolution inside such fibers and find a number of unique features such as the position and the spectral bandwidth of the dispersive wave that change with the location of the ZNW.

We discuss the failure of the Markov approximation in the description of atom-surface fluctuation-induced interactions, both in equilibrium (Casimir-Polder forces) and out of equilibrium (quantum friction). Using general theoretical arguments, we show that the Markov approximation can lead to erroneous predictions of such phenomena with regard to both strength and functional dependencies on system parameters. In particular, we show that the long-time power-law tails of two-time dipole correlations and their corresponding low-frequency behavior, neglected in the Markovian limit, affect the prediction of the force. Our findings highlight the importance of non-Markovian effects in dispersion interactions.

We present observable lower bounds for several bipartite entanglement measures including entanglement of formation, geometric measure of entanglement, concurrence, convex-roof extended negativity, and $G$ concurrence. The lower bounds facilitate estimates of these entanglement measures for arbitrary finite-dimensional bipartite states. Moreover, these lower bounds can be calculated analytically from the expectation value of a single observable. Based on our results, we use several real experimental measurement data to get lower bounds of entanglement measures for these experimentally realized states. In addition, we also study the relations between entanglement measures.

We consider continuous quantum measurement of a superconducting qubit in the circuit QED setup with a moderate bandwidth of the measurement resonator, i.e., when the “bad-cavity” limit is not applicable. The goal is a simple description of the quantum evolution due to measurement, i.e., the measurement backaction. Extending the quantum Bayesian approach previously developed for the bad-cavity regime, we show that the evolution equations remain the same, but now they should be applied to the entangled qubit-resonator state, instead of the qubit state alone. The derivation uses only elementary quantum mechanics and basic properties of coherent states, thus being accessible to nonexperts.