We try to characterize the statistics of multipartite entanglement of the random states of an $n$-qubit system. Unable to solve the problem exactly we generalize it, replacing complex numbers with real vectors with $N_c$ components (the original problem is recovered for $N_c=2$). Studying the leading diagrams in the $\text{large}-N_c$ approximation, we unearth the presence of a phase transition and, in an explicit example, show that the so-called entanglement frustration disappears in the $\text{large}-N_c$ limit.

We study the thermalization of an elementary quantum system modeled by a two-level atom interacting with stationary electromagnetic fields out of thermal equilibrium near a dielectric slab. The slab is held at a temperature different from that of the region where the atom is located. We find that when the slab is nonabsorbing and nondispersive, out-of-thermal-equilibrium effects exist only when its thickness is infinite. In other words, no out-of-thermal-equilibrium effects appear for a real dielectric slab of a finite thickness $d$. Furthermore, a finite thick dielectric slab with a tiny imaginary part in the relative permittivity $\mathrm{Im}\epsilon$ behaves like a half-space dielectric substrate if $\frac{\mathrm{Im}\epsilon }{\sqrt{\mathrm{Re}\epsilon -1}}\frac{d}{{\lambda }_0}>1$ is satisfied, where ${\lambda }_0$ is the transition wavelength of the atom. This condition can serve as a guide for an experimental verification, using a dielectric substrate of a finite thickness, of the effects that arise from out-of-thermal-equilibrium fluctuations with a half-space (infinite thickness) dielectric.

An amplitude-modulated near-infrared laser pulse synchronized to a 14-GHz microwave field is used to excite atoms to the vicinity of the ionization limit at specific phases of the microwave field. When the laser is tuned above and below the ionization limit, phase-dependent modulation is observed in the recombination and ionization, respectively. The phase-dependent modulation is 10% of the total excitation, far greater than the 0.1% modulation observed with single-picosecond laser pulse excitation, and in agreement with calculations based on coherent excitation over several microwave cycles [Phys. Rev. Lett. 95, 013001 (2005)].

For a quantum system controlled by an external field, time-optimal control is referred to as the shortest-time-duration control that can still permit maximizing an objective function $J$, which is especially a desirable goal for engineering quantum dynamics against decoherence effects. However, since rigorously finding a time-optimal control is usually very difficult and in many circumstances the control is only required to be sufficiently short and precise, one can design algorithms seeking such suboptimal control solutions for much reduced computational effort. In this paper, we propose an iterative algorithm for finding near-time-optimal control in a high level set (i.e., the set of controls that achieves the same value of $J$) that can be arbitrarily close to the global optima. The algorithm proceeds seeking to decrease the time duration $T$ while the value of $J$ remains invariant, until $J$ leaves the level-set value; the deviation of $J$ due to numerical errors is corrected by gradient climbing that brings the search back to the level-set $J$ value. Since the level set is very close to the maximum value of $J$, the resulting control solution is nearly time optimal with manageable precision. Numerical examples demonstrate the effectiveness and general applicability of the algorithm.

An ultracold Fermi atomic gas at unitarity presents universal properties that in the dilute limit can be well described by a contact interaction. By employing a guiding function with correct boundary conditions and making simple modifications to the sampling procedure we are able to calculate the properties of a true contact interaction with the diffusion Monte Carlo method. The results are obtained with small variances. Our calculations for the Bertsch and contact parameters are in reasonable agreement with published experiments. The possibility of using a more faithful description of ultracold atomic gases can help uncover additional features of ultracold atomic gases. In addition, this work paves the way to perform quantum Monte Carlo calculations for other systems interacting with contact interactions, where the description using potentials with finite effective range might not be accurate.

We present, characterize, and apply the architecture of a photonic quantum interface between the near infrared and telecom spectral regions. A singly resonant optical parametric oscillator (OPO) operated below threshold, in combination with external filters, generates high-rate ($>2.5\times {10}^6{\mathrm{s}}^{-1}$) narrowband photon pairs ($\sim 7$ MHz bandwidth); the signal photons are tuned to resonance with an atomic transition in ${\mathrm{Ca}}^{+}$, while the idler photons are at telecom wavelength. Interface operation is demonstrated through high-rate absorption of single photons by a single trapped ion ($\sim 670{\mathrm{s}}^{-1}$), heralded by coincident telecom photons.

For a closed quantum system, a dynamical invariant is defined as an operator whose expectation value is a constant. In this paper, we extend the concept of dynamical invariants from closed systems to open systems. A dynamical equation for invariants (the dynamical invariant condition) is derived for Markovian dynamics. Different from dynamical invariants of closed quantum systems, the time evolution of dynamical invariants of open quantum systems is no longer unitary, and eigenvalues of any invariant are time dependent in general. Since any Hermitian operator which can fulfill the dynamical invariant condition is a dynamical invariant, we construct a type of special dynamical invariant of which a part of the eigenvalues is still constant. The dynamical invariants in the subspace spanned by these eigenstates thus evolve unitarily.

The important role of geometric phases in searches for a permanent electric dipole moment of the neutron, using Ramsey separated oscillatory field nuclear magnetic resonance, was first noted by Commins [Am. J. Phys. 59, 1077 (1991)] and investigated in detail by Pendlebury et al. [Phys. Rev. A 70, 032102 (2004)]. Their analysis was based on the Bloch equations. In subsequent work using the spin-density matrix, Lamoreaux and Golub [Phys. Rev. A 71, 032104 (2005)] showed the relation between the frequency shifts and the correlation functions of the fields seen by trapped particles in general fields (Redfield theory). More recently, we presented a solution of the Schrödinger equation for spin-$1/2$ particles in circular cylindrical traps with smooth walls and exposed to arbitrary fields [A. Steyerl et al., Phys.  Rev. A 89, 052129 (2014)]. Here, we extend this work to show how the Redfield theory follows directly from the Schrödinger equation solution. This serves to highlight the conditions of validity of the Redfield theory, a subject of considerable discussion in the literature [e.g., M. P. Nicholas et al., Prog. Nucl. Magn. Reson. Spectrosc. 57, 111 (2010)]. Our results can be applied where the Redfield result no longer holds, such as observation times on the order of or shorter than the correlation time and nonstochastic systems, and thus we can illustrate the transient spin dynamics, i.e., the gradual development of the shift with increasing time subsequent to the start of the free precession. We consider systems with rough, diffuse reflecting walls, cylindrical trap geometry with arbitrary cross section, and field perturbations that do not, in the frame of the moving particles, average to zero in time. We show by direct, detailed, calculation the agreement of the results from the Schrödinger equation with the Redfield theory for the cases of a rectangular cell with specular walls and of a circular cell with diffuse reflecting walls.

Tunneling ionization is one of the fundamental processes for molecules in intense laser fields, and the tunnel-ionized molecules are in various electronic states. Here, we report an experimental study of the population dynamics of ${{\mathrm{N}}_2}^{+}\left(B{}^2{{\mathrm{\Sigma }}_u}^{+}\right)$ and ${{\mathrm{N}}_2}^{+}\left(X{}^2{{\mathrm{\Sigma }}_g}^{+}\right)$ generated in intense femtosecond laser fields by simultaneously measuring the fluorescence emission spectra and the transmission spectra. The results reveal that the population inversion exists between ${{\mathrm{N}}_2}^{+}\left(B{}^2{{\mathrm{\Sigma }}_u}^{+}\right)$ and ${{\mathrm{N}}_2}^{+}\left(X{}^2{{\mathrm{\Sigma }}_g}^{+}\right)$. But the population difference is much smaller than the absolute population of ${{\mathrm{N}}_2}^{+}\left(B{}^2{{\mathrm{\Sigma }}_u}^{+}\right)$. The present study provides insight into understanding the observation of the generation of an air laser from the tunnel-ionized nitrogen molecules, which has been attributed to the population inversion between ${{\mathrm{N}}_2}^{+}\left(B{}^2{{\mathrm{\Sigma }}_u}^{+}\right)$ and ${{\mathrm{N}}_2}^{+}\left(X{}^2{{\mathrm{\Sigma }}_g}^{+}\right)$ in intense femtosecond laser fields at 800-nm wavelengths.

Deep laser cooling of ${}^{24}\mathrm{Mg}$ atoms has been theoretically studied. We propose a two-stage sub-Doppler cooling strategy using electrodipole transition $3{}^3{P}_2\to 3{}^3{D}_3$ ($\lambda =383.8$ nm). The first stage implies exploiting magneto-optical trap with ${\sigma }^{+}$ and ${\sigma }^{-}$ light beams, while at the second stage lin $\perp$ lin molasses is used. We focus on achieving a large number of ultracold atoms ($T_{\mathrm{eff}}<10 \mu \mathrm{K}$) in a cold-atomic cloud. The calculations have been based on quantum treatment, taking into full account the recoil effect and beyond many widely used approximations. Steady-state values of average kinetic energy and linear momentum distributions of cold atoms have been analyzed for various light-field intensities and frequency detunings. The results of conducted quantum analysis have been significantly different from the results achieved under a semiclassical approximation based on the Fokker-Planck equation. The second cooling stage allows achieving sufficiently lower kinetic energies of the atomic cloud as well as increased fraction of ultracold atoms at certain conditions compared to the first one. We hope that the obtained results can help in overcoming current experimental problems in deep cooling of ${}^{24}\mathrm{Mg}$ atoms by means of laser field. Cold magnesium atoms cooled in a large amount to several $\mu \mathrm{K}$ are of huge interest to, for example, quantum metrology and to other many-body cold-atoms physics.

We present an exact numerical study of the scaling of density and momentum distribution functions of harmonically trapped one-dimensional bosons with repulsive contact interactions at zero and finite temperatures. We use path integral quantum Monte Carlo with worm updates in our calculations at finite interaction strengths, and the Bose-Fermi mapping in the Tonks-Girardeau regime. We discuss the homogeneous case and, within the local density approximation, use it to motivate the scaling in the presence of a harmonic trap. For the momentum distribution function, we pay special attention to the high momentum tails and their $k^{-4}$ asymptotic behavior.

We report on the observation of weakly bound dimers of bosonic dysprosium with a strong universal $s$-wave halo character, associated with broad magnetic Feshbach resonances. These states surprisingly decouple from the chaotic background of narrow resonances, persisting across many such narrow resonances. In addition they show the highest reported magnetic moment $\mu \simeq 20{\mu }_{\mathrm{B}}$ of any ultracold molecule. We analyze our findings using a coupled-channel theory taking into account the short range van der Waals interaction and a correction due to the strong dipole moment of dysprosium. We are able to extract the scattering length as a function of magnetic field associated with these resonances and obtain a background scattering length $a_{\mathrm{bg}}=91\left(16\right)a_0$. These results offer prospects of a tunability of the interactions in dysprosium, which we illustrate by observing the saturation of three-body losses.

In the present article explicit expressions for the decay rate and energy-level shifts of an atom in the presence of an ideal conducting wedge, two parallel plates, and a half sheet are obtained in the framework of the canonical quantization approach. The angular and radial dependences of the decay rate for different atomic polarizations of an excited atom and also of the energy-level shifts are depicted and discussed. The consistency of the present approach in some limiting cases is investigated by comparing the relevant results obtained here to the previously reported results.

The implementation of optimal statistical inference protocols for high-dimensional quantum systems is often computationally expensive. To avoid the difficulties associated with optimal techniques, here I propose an alternative approach to quantum estimation and detection based on Volterra filters. Volterra filters have a clear hierarchy of computational complexities and performances, depend only on finite-order correlation functions, and are applicable to systems with no simple Markovian model. These features make Volterra filters appealing alternatives to optimal nonlinear protocols for the inference and control of complex quantum systems. Applications of the first-order Volterra filter to continuous-time quantum filtering, the derivation of a Heisenberg-picture uncertainty relation, quantum state tomography, and qubit readout are discussed.

Quantum theory is known to be nonlocal in the sense that separated parties can perform measurements on a shared quantum state to obtain correlated probability distributions, which cannot be achieved if the parties share only classical randomness. Here we find that the set of distributions compatible with sharing quantum states subject to some sufficiently restricted dimension is neither convex nor a superset of the classical distributions. We examine the relationship between quantum distributions associated with a dimensional constraint and classical distributions associated with limited shared randomness. We prove that quantum correlations are convex for certain finite dimension in certain Bell scenarios and that they sometimes offer a dimensional advantage in realizing local distributions. We also consider if there exist Bell scenarios where the set of quantum correlations is never convex with finite dimensionality.

Weak values, introduced more than 25 years ago, underwent a metamorphosis from a theoretical curiosity to a powerful resource in photonics for exploring foundations of quantum mechanics, as well as a practical laboratory tool. Due to the tiny coherence volume of particles used in matter-wave optics, a straightforward implementation of weak measurements is not feasible. We have overcome this hurdle by developing a method to weakly measure a massive particle's spin component. A neutron optical approach is realized by utilizing neutron interferometry, where the neutron's spin is coupled weakly to its spatial degree of freedom. Here, we present how one can fully characterize the weak value of the Pauli spin operator ${\widehat{\sigma }}_z$ of neutrons by extracting its real and imaginary components, as well as its modulus. The results show good agreement with theoretical predictions and demonstrate that the (spin) weak value is actually accessible for a purely quantum system of massive particles.

We present a systematic method to introduce free parameters in sets of mutually unbiased bases. In particular, we demonstrate that any set of $m$ real mutually unbiased bases existing in dimension $N>2$ admits the introduction of $(m-1)N/2$ free parameters that cannot be absorbed by a global unitary operation. As consequence, there are $m=k+1$ mutually unbiased bases in every dimension $N=k^2$ with $k^3/2$ free parameters, where $k$ is even. We explicitly construct the maximal set of triplets of mutually unbiased bases for two-qubit systems and triplets, quadruplets, and quintuplets of mutually unbiased bases with free parameters for three-qubit systems. Furthermore, we study the richness of the entanglement structure of such bases and provide the quantum circuits required to implement all these bases with free parameters in the laboratory. We also show that the free parameters introduced can be controlled by a single party of the system. Finally, we find the upper bound for the maximal number of real and complex mutually unbiased bases existing in every dimension. This proof is simple, short, and considers basic matrix algebra.

We demonstrate the robustness of BosonSampling against imperfections in the linear optical network that cause a small deviation in the matrix it implements. We show that applying a noisy matrix $\tilde{U}$ that is within $\epsilon$ of the desired matrix $U$ in operator norm leads to an output distribution that is within $\epsilon n$ of the desired distribution in variation distance, where $n$ is the number of photons. This lets us derive a sufficient tolerance for beam splitters and phase shifters in the network. This result only concerns errors that result from the network encoding a different unitary than desired and not from other sources of noise such as photon loss and partial distinguishability.