We study the superfluidity of single-component dipolar Fermi gases in three dimensions using a pairing fluctuation theory, within the context of BCS-BEC crossover. The transition temperature $T_c$ for the dominant $p_z$ wave superfluidity exhibits a remarkable reentrant behavior as a function of the pairing strength induced by the dipole-dipole interaction (DDI), which leads to an anisotropic pair dispersion. The anisotropy and the long-range nature of the DDI cause $T_c$ to vanish for a narrow range of intermediate interaction strengths, where a pair density wave emerges as the ground state. The superfluid density and thermodynamics below $T_c$, along with the density profiles in a harmonic trap, are investigated as well. Implications for experiments are discussed.

The quantum state of motion of a large and rotating polar molecule can lose coherence through the collisions with gas atoms. We show how the associated quantum master equation for the center of mass can be expressed in terms of the orientationally averaged differential and total scattering cross sections, for which we provide approximate analytic expressions. The master equation is then utilized to quantify collisional decoherence in a interference experiment with polar molecules.

We show that generalized dissipative optomechanical coupling enables a direct quantum measurement of speed of a free test mass. An optical detection of a weak classical mechanical force based on this interaction is proposed. The sensitivity of the force measurement can be better than the standard quantum limit.

The time-local master equation for a driven boson system interacting with a boson environment is derived by way of a time-local Heisenberg-Langevin equation. Extension to the driven qubit fails—except for weak excitation—due to the lost linearity of the system-environment interaction. We show that a reported time-local master equation for the driven qubit is incorrect. As a corollary to our demonstration, we also uncover odd asymptotic behavior in the “repackaged” time-local dynamics of a system driven to a far-from-equilibrium steady state: the density operator becomes steady while time-dependent coefficients oscillate (with periodic singularities) forever.

We explore the phase diagram of the $\mathrm{SU}\left(N\right)$ Hubbard models describing fermionic alkaline-earth-metal atoms in a square optical lattice with, on average, one atom per site, using a slave rotor mean-field approach. We find that the chiral spin liquid (CSL) predicted for $N\ge 5$ and large interactions passes through a fractionalized state with a spinon Fermi surface as interactions are decreased before transitioning to a weakly interacting metal. We show that by adding a uniform artificial gauge field with $2\pi /N$ flux per plaquette, the CSL becomes the ground state for all $N\ge 3$ at intermediate interactions, persists to weaker interactions, and exhibits a larger spin gap. For $N\ge 5$ we find the CSL is the ground state everywhere the system is a Mott insulator. The gauge field stabilization of the CSL at lower interactions, and thus at weaker lattice depths, together with the increased spin gap, can relax the temperature constraints required for its experimental realization in ultracold atom systems.

An interferometer—no matter how clever the design—cannot reveal both the wave and the particle behavior of a quantum system. This fundamental idea has been captured by inequalities, so-called wave-particle duality relations (WPDRs), that upper bound the sum of the fringe visibility (wave behavior) and path distinguishability (particle behavior). Another fundamental idea is Heisenberg's uncertainty principle, stating that some pairs of observables cannot be known simultaneously. Recent work has unified these two principles for two-path interferometers. Here we extend this unification to $n$-path interferometers, showing that WPDRs correspond to a modern formulation of the uncertainty principle stated in terms of entropies. Furthermore, our unification provides a framework for solving an outstanding problem of how to formulate universally valid WPDRs for interferometers with more than two paths, and we employ this framework to derive some novel WPDRs.

Properties of random mixed states of dimension $N$ distributed uniformly with respect to the Hilbert-Schmidt measure are investigated. We show that for large $N$, due to the concentration of measure, the trace distance between two random states tends to a fixed number $\tilde{D}=1/4+1/\pi$, which yields the Helstrom bound on their distinguishability. To arrive at this result, we apply free random calculus and derive the symmetrized Marchenko-Pastur distribution, which is shown to describe numerical data for the model of coupled quantum kicked tops. Asymptotic value for the root fidelity between two random states, $\sqrt{F}=\frac{3}{4}$, can serve as a universal reference value for further theoretical and experimental studies. Analogous results for quantum relative entropy and Chernoff quantity provide other bounds on the distinguishablity of both states in a multiple measurement setup due to the quantum Sanov theorem. We study also mean entropy of coherence of random pure and mixed states and entanglement of a generic mixed state of a bipartite system.

We have employed both the $Z$-vector method and the expectation-value approach in the relativistic coupled-cluster framework to calculate the scalar-pseudoscalar (S-PS) $\mathcal{P},\mathcal{T}$-odd interaction constant $W_{\mathrm{s}}$ and the effective electric field $E_{\mathrm{eff}}$ experienced by the unpaired electron in the ground electronic state of RaF. Further, the magnetic hyperfine structure constants of ${}^{223}\mathrm{Ra}$ in RaF and ${}^{223}\mathrm{Ra}^{+}$ are also calculated and compared with the experimental values wherever available to judge the extent of the accuracy obtained with the employed methods. The outcome of our study reveals that the $Z$-vector method is superior to the expectation-value approach in terms of accuracy obtained for the calculation of ground-state property. The $Z$-vector calculation shows that RaF has a high $E_{\mathrm{eff}}$ (52.5 GV/cm) and $W_{\mathrm{s}}$ (141.2 kHz), which makes it a potential candidate for the electric dipole moment of the electron (eEDM) experiment. An estimation of uncertainty associated with our final results is made, and it is found that it lies below 10%.

Universal properties of Efimov states for some triatomic systems composed by one light and two heavy atoms are investigated using the finite-range model potentials. We have successfully obtained accurate values of binding energies and sizes for three successive Efimov states. Compared with the predicted scaling constants of the zero-range theory, the ground Efimov states are found to have the largest finite-range corrections. There exists a universal size-binding momentum relation for Efimov states which can be described by the formula ${\mathcal{R}}_{n^{*}}{k}_{n^{*}}=\sqrt{(1+s_0^2)/3}$ derived with zero-range approximation. It is found that for the Efimov states that have large scaled sizes, their size-binding momentum relations follow the universal formula well. Our calculations demonstrate that size is an important characteristic in determining the universalities of Efimov states.

We consider theoretically materials whose electromagnetic properties possess parity-time $\left(\mathcal{PT}\right)$ symmetry and are periodic in two dimensions. When designed for optical frequencies such structures are commonly known as two-dimensional (2D) photonic crystals. With the addition of $\mathcal{PT}$ symmetry the optical modes of 2D photonic crystals exhibit thresholdless spontaneous $\mathcal{PT}$-symmetry breaking near the Brillouin zone boundary, which is analogous to what has previously been studied in $\mathcal{PT}$-symmetric structures with one-dimensional periodicity. Consistent with previous work, we find that spontaneous $\mathcal{PT}$-symmetry breaking occurs at band crossings in the photonic dispersion diagram. Due to the extra spatial degree of freedom in 2D periodic systems, their band structures contain more band crossings and higher-order degeneracies than their one-dimensional counterparts. This work provides a comprehensive theoretical analysis of spontaneous $\mathcal{PT}$-symmetry breaking at these points in the band structure. We find that, as in the case of one-dimensional structures, photonic band gaps exist at $k=0$. We also find that at points of degeneracy with order higher than 2, bands merge pairwise to form broken-$\mathcal{PT}$-symmetry supermodes. If the degeneracy order is even, this means multiple pairs of bands can form distinct (nondegenerate) broken-symmetry supermodes. If the order of degeneracy is odd, at least one of the bands will have protected $\mathcal{PT}$ symmetry. At other points of degeneracy, we find that the $\mathcal{PT}$ symmetry of the modes may be protected and we provide a spatial mode symmetry argument to explain this behavior. Finally, we identify a point at which two broken-$\mathcal{PT}$-symmetry supermodes become degenerate, creating a point of fourfold degeneracy in the broken-$\mathcal{PT}$-symmetry regime.

We present an in-depth study of electromagnetic wave propagation in a temporal photonic crystal, namely, a nonconducting medium whose permittivity $\varepsilon \left(t\right)$ and/or permeability $\mu \left(t\right)$ are modulated periodically by unspecified agents (these modulations not necessarily being in phase). Maxwell's equations lead to an eigenvalue problem whose solution provides the dispersion relation $\omega \left(k\right)$ for the waves that can propagate in such a dynamic medium. This is a generalization of previous work [J. R. Zurita-Sánchez and P. Halevi, Phys. Rev. A 81, 053834 (2010)] that was restricted to the electric modulation $\varepsilon \left(t\right)$. For our numerical work (only) we assumed the harmonic modulations $\varepsilon \left(t\right)=\overline{\varepsilon }[1+m_{\varepsilon }sin\left(\mathrm{\Omega }t\right)]$ and $\mu \left(t\right)=\overline{\mu }[1+m_{\mu }sin(\mathrm{\Omega }t+\theta )]$, where $\mathrm{\Omega }$ is the circular modulation frequency; $m_{\varepsilon }$ and $m_{\mu }$ are, respectively, the strengths of the electric and magnetic modulations; and $\theta$ is the phase difference between these modulations. An analytic calculation for weak modulations $(m_{\varepsilon }\ll 1,m_{\mu }\ll 1)$ leads to two $k$ bands, $k_1\left(\omega \right)$ and $k_2\left(\omega \right)$, that are separated by a $k$ gap. If the modulations are in phase $(\theta =0)$, this gap is proportional to $|m_{\varepsilon }-m_{\mu }|$, while the gap is proportional to $(m_{\varepsilon }+m_{\mu })$ if the modulations are out of phase $(\theta =\pi )$. The gap thus disappears for equal, in-phase, modulations $(m_{\varepsilon }=m_{\mu })$. An exact solution of the eigenvalue equation confirms that these approximations hold reasonably well even for moderate modulations. In fact, there are no $k$ gaps for equal modulations even if these are very strong $(m_{\varepsilon ,\mu }\lesssim 1)$. The photonic band structure $k\left(\omega \right)$ is periodic in $\omega$, with period $\mathrm{\Omega }$, and there is an infinite number of bands $k_1\left(\omega \right)$, $k_2\left(\omega \right),...$ Further, by allowing $\varepsilon \left(t\right)$ and $\mu \left(t\right)$ to have imaginary parts, we examined the effects of damping $\left[\mathrm{Im}k\right(\omega \left)\right]$ on the $k$ bands. We also determined the optical response of a temporal photonic crystal slab, applying the above harmonic model for $\varepsilon \left(t\right)$ and $\mu \left(t\right)$. The reflected and transmitted light represent a frequency comb of frequencies $\omega$, $|\omega \pm \mathrm{\Omega }|$, $|\omega \pm 2\mathrm{\Omega }|,...$ The transmission coefficients ${\mathcal{T}}_n\left(\omega \right)$ for these harmonics $n\mathrm{\Omega }$ of the modulation frequency strongly depend on the parameters $m_{\varepsilon }$, $m_{\mu }$, and $\theta$, as well as on the thickness of the slab. Moreover, they can much exceed unity, as a result of energy transfer from the source of modulation. In a particularly interesting case, ${\mathcal{T}}_n\left(\omega \right)$ exhibits oscillations with peaks that resemble parametric resonances, rather than the usual Fabry-Perot resonances.

Parity-time ($\mathcal{PT}$) symmetric systems, which rely on the balanced gain-loss condition and render the Hamiltonian non-Hermitian, have provided a new platform to engineer effective light-matter interactions in recent years. Here we explore the high-order sideband features of the output fields obtained from a $\mathcal{PT}$-symmetric optical system consisting of a passive nonlinear cavity coupled to an active linear cavity. By employing a perturbation technique, we derive analytic formulas used to determine the nonlinear transmission coefficient of optical second-order sideband in this structure. Using experimentally achievable parameters, it is clearly shown that the efficiency of the second-order sideband generation can be greatly enhanced in the $\mathcal{PT}$-symmetric dimer, extremely in the vicinity of the transition point from unbroken- to broken-$\mathcal{PT}$ regimes. Moreover, we further analyzed the influences of the system parameters, including the photon-tunneling rate between two cavities, Kerr nonlinearity strength, and optical detuning, on the second-order sideband generation. Subsequently we investigate the higher-order sideband output spectrum by numerical simulations, where the sideband amplitude also is largely enhanced in the $\mathcal{PT}$-symmetric arrangement, compared with the passive-passive double-cavity system. Our obtained results provide a new avenue for acquiring optical high-order sidebands and operating light, which may inspire further applications in chip-scale optical communications and optical frequency combs.

The expressions for the optical drag force, the equilibrium kinetic energy, and the diffusion constant of an electric dipole in a light field consisting of electromagnetic plane waves with polarizations randomly distributed and fluctuating phases are obtained. The drag force is proportional to the extinction cross section of the dipole and to the intensity. The diffusion constant does not depend on the amplitude of the electromagnetic field and is proportional to the time interval between fluctuations. Numerical simulations for the dynamics of a resonant dipole, initially at rest, show the crossover between the superdiffusive and the diffusive regimes theoretically predicted.

We observe the three-photon correlation in nonclassical light sources by using an indirect measurement scheme based on the dead-time effect of photon-counting detectors. We first develop a general theory which enables us to extract the three-photon correlation from the two-photon correlation of an arbitrary light source measured with detectors with finite dead times. We then confirm the validity of our measurement scheme in experiments done with a cavity-QED microlaser operating with a large intracavity mean photon number exhibiting both sub- and super-Poissonian photon statistics. The experimental results are in good agreement with the theoretical expectation. Our measurement scheme provides an alternative approach for $N$-photon correlation measurement employing $(N-1)$ detectors and thus a reduced measurement time for a given signal-to-noise ratio, compared to the usual scheme requiring $N$ detectors.

We present a detailed theoretical analysis of a Fock-state filter based on the photon-number-dependent group delay in cavity-induced transparency proposed by Nikoghosyan and Fleischhauer [G. Nikoghosyan and M. Fleischhauer, Phys. Rev. Lett. 105, 013601 (2010)]. We derive a general expression for the propagation velocity of different photon-number components of a light pulse interacting with an optically dense ensemble of three-level atoms coupled to a resonator mode under conditions of cavity-induced transparency. These predictions are compared to numerical simulations of the propagation of few-photon wave packets, and an estimation for experimental realization is made.

We study a parity-time–$(\mathcal{PT}-)$ symmetric ring lattice, with one pair of balanced gain and loss located at opposite positions. The system remains $\mathcal{PT}$-symmetric when threaded by a magnetic flux; however, the $\mathcal{PT}$ symmetry is sensitive to the magnetic flux in the presence of a large balanced gain and loss, or in a large system. We find a threshold gain or loss above which any nontrivial magnetic flux breaks the $\mathcal{PT}$ symmetry. We obtain the maximally tolerable magnetic flux for the exact $\mathcal{PT}$-symmetric phase, which is approximately linearly dependent on a weak gain or loss.

We calculate the density shift and broadening of selected dipole transition lines of pionic helium in gaseous helium at low temperatures up to $T=12$ K and pressure up to a few bars. In the approximation of binary collisions the shift and broadening depend linearly on the density; we evaluate the slope of this linear dependence for a few spectral lines of known experimental interest and also investigate its temperature dependence. We find a blueshift of the resonance frequencies of the $(n,l)=(16,15)\to (16,14), (17,16)\to (17,15)$, and $(16,15)\to (17,14)$ unfavored transitions and a redshift for the favored one, $(17,16)\to (16,15)$. The results are intended to significantly increase the efficiency of the laser spectroscopy investigations of pionic helium and help with the interpretation of the experimental data.

The behavior of a spin undergoing Larmor precession in the presence of fluctuating fields is of interest to workers in many fields. The fluctuating fields cause frequency shifts and relaxation which are related to their power spectrum, which can be determined by taking the Fourier transform of the auto-correlation functions of the field fluctuations. Recently we have shown how to calculate these correlation functions for all values of mean-free path (ballistic to diffusive motion) in finite bounded regions by using the model of persistent continuous time random walks (CTRW) for particles subject to scattering by fixed (frozen) scattering centers so that the speed of the moving particles is not changed by the collisions. In this work we show how scattering with energy exchange from an ensemble of scatterers in thermal equilibrium can be incorporated into the CTRW. We present results for 1, 2, and 3 dimensions. The results agree for all these cases contrary to the previously studied “frozen” models. Our results for the velocity autocorrelation function show a long-time tail $(\sim t^{-1/2})$, which we also obtain from conventional diffusion theory, with the same power, independent of dimensionality. Our results are valid for any Markovian scattering kernel as well as for any kernel based on a scattering cross section $\sim 1/v$.

We compute the exact exchange-correlation potential of the time-dependent density-functional theory (TDDFT) for the correlated process of autoionization. The potential develops barriers which regulate the autoionization rate. TDDFT employing known and practicable exchange-correlation potentials does not capture any autoionization dynamics. Approximate exchange-correlation potentials capturing such dynamics would necessarily require memory effects and are unlikely to be developed, as will be illustrated.