In this paper, we propose an experimentally feasible scheme that the superconducting quantum interference devices are coupled with a high-quality cavity supporting a single-mode photon, to realize an effective Dicke model. By using several hundred artificial two-level atoms, the strong coupling regime can be successfully achieved. Moreover, in our proposal the superradiant phase transition for this model can be well controlled by the frequency of external magnetic flux when the superconducting charge qubits work at their optimal point, in which the qubits can be mostly immune from charge noise produced by uncontrollable charge fluctuations. Finally, we propose to observe this phase transition by detecting the intracavity intensity in terms of a heterodyne detector out of the cavity.

We investigate experimentally and theoretically plane-mirror Fabry-Perot resonators filled by photonic crystals, i.e., with periodic intracavity refraction index modulation. We show that the diffraction properties of such resonators can be manipulated, resulting in sub- and superdiffractive dynamics of light in the resonator, and in hyperbolic angular transmission profiles.

In this paper, we present a fully fiber-based one-way quantum-key-distribution (QKD) system implementing the Gaussian-modulated coherent-state (GMCS) protocol. The system employs a double Mach-Zehnder interferometer (MZI) configuration in which the weak quantum signal and the strong local oscillator (LO) go through the same fiber between Alice and Bob, and are separated into two paths inside Bob’s terminal. To suppress the LO leakage into the signal path, which is an important contribution to the excess noise, we implemented a scheme combining polarization and frequency multiplexing, achieving an extinction ratio of 70 dB. To further minimize the system excess noise due to phase drift of the double MZI, we propose that, instead of employing phase feedback control, one simply let Alice remap her data by performing a rotation operation. We further present noise analysis both theoretically and experimentally. Our calculation shows that the combined polarization and frequency multiplexing scheme can achieve better stability in practice than the time-multiplexing scheme, because it allows one to use matched fiber lengths for the signal and the LO paths on both sides of the double MZI, greatly reducing the phase instability caused by unmatched fiber lengths. Our experimental noise analysis quantifies the three main contributions to the excess noise, which will be instructive to future studies of the GMCS QKD systems. Finally, we demonstrate, under the “realistic model” in which Eve cannot control the system within Bob’s terminal, a secure key rate of $0.3\text{bit}∕\text{pulse}$ over a 5km fiber link. This key rate is about two orders of magnitude higher than that of a practical Bennett-Brassard 1984 protocol QKD system.

We investigate the temporal dynamics of Doppler cooling of an initially hot single trapped atom in the weak-binding regime using a semiclassical approach. We develop an analytical model for the simplest case of a single vibrational mode for a harmonic trap, and show how this model allows us to estimate the initial energy of the trapped particle by observing the time-dependent fluorescence during the cooling process. The experimental implementation of this temperature measurement provides a way to measure atom heating rates by observing the temperature rise in the absence of cooling. This method is technically relatively simple compared to conventional sideband detection methods, and the two methods are in reasonable agreement. We also discuss the effects of rf micromotion, relevant for a trapped atomic ion, and the effect of coupling between the vibrational modes on the cooling dynamics.

We discuss the properties of ultracold Rydberg atoms in a Ioffe-Pritchard magnetic field configuration. The derived two-body Hamiltonian unveils how the large size of Rydberg atoms affects their coupling to the inhomogeneous magnetic field. The properties of the compound electronic and center of mass quantum states are thoroughly analyzed. We find very tight confinement of the center of mass motion in two dimensions to be achievable while barely changing the electronic structure compared to the field free case. This paves the way for generating a one-dimensional ultracold Rydberg gas.

In this paper we develop an analytic expression for the critical temperature for a gas of ideal bosons in a combined harmonic lattice potential, relevant to current experiments using optical lattices. We give corrections to the critical temperature arising from effective mass modifications of the low energy spectrum, finite size effects, and excited band states. We compute the critical temperature using numerical methods and compare to our analytic result. We study condensation in an optical lattice over a wide parameter regime and demonstrate that the critical temperature can be increased or reduced relative to the purely harmonic case by adjusting the harmonic trap frequency. We show that a simple numerical procedure based on a piecewise analytic density of states provides an accurate prediction for the critical temperature.

We study the dilute fermion gas with pairing between two species and unequal concentrations in a harmonic trap using the mean-field theory and the local density approximation. We found that the system can exhibit a superfluid shell structure sandwiched by the normal fermions. This superfluid shell structure occurs if the mass ratio is larger than a certain critical value, which increases from the weak-coupling BCS region to the strong-coupling Bose-Einstein condensation (BEC) side. In the strong-coupling BEC regime, the radii of the superfluid phase are less sensitive to the mass ratios and are similar to the case of pairing with equal masses. However, the lighter leftover fermions are easier to mix with the superfluid core than the heavier ones. A partially polarized superfluid can be found if the majority fermions are lighter, whereas phase separation is still found if they are heavier.

Ultracold Fermi gases near the unitary limit are studied in the framework of effective field theory. It is shown that, while one can obtain a reasonable description of the universal proportionality constants both in the narrow and the broad Feshbach resonance limits, the requirement of the reparametrization invariance leads to the appearance of the three-body forces needed to cancel the off-shell uncertainties. The size of the uncertainties is estimated.

Laser-pulse filamentation in Kerr media induced by a strongly elliptic input beam leads to breakup into a periodic array of filaments. In the plane of the filament array we observe strong Stokes and anti-Stokes emission at large angles. For 1 ps input pulses the measured angles are found to support two different phase-matching configurations: one nontransversally phase matched and the other perfectly phase matched. Shorter 200 fs pulses give rise to group-velocity-matched Raman conversion.

We discuss the possibility of observing quantum nonlocality using the so-called mode entanglement, analyzing the differences between different types of particles in this context. We first discuss the role of coherent states in such experiments, and we comment on the existence of coherent states in nature. The discussion of coherent states naturally raises questions about the role of particle statistics in this problem. Although the Pauli exclusion principle precludes coherent states with a large number of fermionic particles, we find that a large number of fermionic coherent states, each containing at most one particle, can be used to achieve the same effect as a bosonic coherent state for the purposes of this problem. The discussion of superselection rules arises naturally in this context, because their applicability to a given situation prohibits the use of coherent states. This limitation particularly affects the scenario that we propose for detecting the mode entanglement of fermionic particles.

The supersymmetric approach in the form of second-order intertwining relations is used to prove the exact solvability of the two-dimensional Schrödinger equation with generalized two-dimensional Morse potential for $a_0=-1∕2$. This two-parametric model is not amenable to the conventional separation of variables, but it is completely integrable: the symmetry operator of fourth order in momenta exists. All bound-state energies are found explicitly, and all corresponding wave functions are built analytically. By means of the shape invariance property, the result is extended to the hierarchy of Morse models with arbitrary integer and half-integer values $a_k=-(k+1)∕2$.

We discuss upper bounds on the rate at which unitary evolution governed by a nonlocal Hamiltonian can generate entanglement in a bipartite system. Given a bipartite Hamiltonian $H$ coupling two finite dimensional particles $A$ and $B$, the entangling rate is shown to be upper bounded by $c\text{log}\left(d\right)\Vert H\Vert$, where $d$ is the smallest dimension of the interacting particles, $\Vert H\Vert$ is the operator norm of $H$, and $c$ is a constant close to 1. Under certain restrictions on the initial state we prove an analogous upper bound for the ancilla-assisted entangling rate with a constant $c$ that does not depend upon dimensions of local ancillas. The restriction is that the initial state has at most two distinct Schmidt coefficients (each coefficient may have arbitrarily large multiplicity). Our proof is based on analysis of a mixing rate—a functional measuring how fast entropy can be produced if one mixes a time-independent state with a state evolving unitarily.

We find tight lower and upper bounds on the entanglement of a superposition of two bipartite states in terms of the entanglement of the two states constituting the superposition. Our upper bound is dramatically tighter than the one presented by Linden et al. [Phys. Rev. Lett. 97, 100502 (2006)] and our lower bound can be used to provide lower bounds on different measures of entanglement such as the entanglement of formation and the entanglement of subspaces. We also find that in the case in which the two states are one-sided orthogonal, the entanglement of the superposition state can be expressed explicitly in terms of the entanglement of the two states in the superposition.

We consider the ground-state entanglement in highly connected many-body systems consisting of harmonic oscillators and spin-$1∕2$ systems. Varying their degree of connectivity, we investigate the interplay between the enhancement of entanglement, due to connections, and its frustration, due to monogamy constraints. Remarkably, we see that in many situations the degree of entanglement in a highly connected system is essentially of the same order as in a low connected one. We also identify instances in which the entanglement decreases as the degree of connectivity increases.

We consider the unambiguous state discrimination (USD) of two mixed quantum states. We study the rank and the spectrum of the elements of an optimal USD measurement. This naturally leads to a partial fourth reduction theorem. This theorem shows that either the failure probability equals its overall lower bound given in terms of the fidelity or a two-dimensional subspace can be split off from the original Hilbert space. We then use this partial reduction theorem to derive the optimal solution for any two equally probable geometrically uniform states ${\rho }_0$ and ${\rho }_1=U{\rho }_0{U}^{†}$, $U^2=\mathbb{1}$, in a four-dimensional Hilbert space. This represents a second class of analytical solutions for USD problems that cannot be reduced to some pure state cases. We apply our result to answer two questions that are relevant in implementations of the Bennett and Brassard 1984 quantum key distribution protocol using weak coherent states.

We have developed and applied an ab initio fully relativistic method for precise calculations of outer-shell transitions in highly charged ions. This method is based on the multiconfiguration Dirac-Fock-Sturm theory in combination with Brillouin-Wigner many-body perturbation theory. We demonstrate the capability of the method through calculations of the $3s$, $3d\to 2p$ transitions in $\mathrm{Fe}\mathrm{XIX}$. The basis set, constructed out of Dirac-Fock and Sturm one-electron wave functions, allows calculations with an accuracy of less than a few ${10}^{-3}\mathrm{\AA }$ for the wavelengths and better than 1% for the oscillator strengths. Some of the transitions given here have not been observed or calculated previously.

We investigate the classical dynamics of a hydrogen atom near a metallic surface in the presence of a uniform electric field. To describe the atom-surface interaction we use a simple electrostatic image model. Owing to the axial symmetry of the system, the $z$-component of the canonical angular momentum $P_{\varphi }$ is an integral and the electronic dynamics is modeled by a two degrees of freedom Hamiltonian in cylindrical coordinates. The structure and evolution of the phase space as a function of the electric field strength is explored extensively by means of numerical techniques of continuation of families of periodic orbits and Poincaré surfaces of section. We find that, due to the presence of the electric field, the atom is strongly polarized through two consecutive pitchfork bifurcations that strongly change the phase space structure. Finally, by means of the phase space transition state theory and the classical spectral theorem, the ionization dynamics of the atom is studied.

Photoassociation of a pair of cold atoms by excitation with a short chirped laser pulse creates a dynamical hole in the initial continuum wave function. This hole is manifested by a void in the pair wave function and a momentum kick. Photoassociation into loosely bound levels of the external well in ${\mathrm{Cs}}_2{0}_g^{-}(6S+6P_{3∕2})$ is considered as a case study. After the pulse, the free evolution of the ground triplet state $a{}^3\Sigma _u^{+}$ wave packet is analyzed. Due to a negative momentum kick, motion to small distances is manifested and a compression effect is pointed out, markedly increasing the density of atom pairs at short distance. A consequence of the hole is the redistribution of the vibrational population in the $a{}^3\Sigma _u^{+}$ state, with population of the last bound level and creation of pairs of hot atoms. The physical interpretation makes use of the time dependence of the mass current and population on each channel to understand the role of the parameters of the photoassociation pulse. By varying such parameters, optimization of the compression effect in the ground-state wave packet is demonstrated. Due to an increase of the short-range probability density by more than two orders of magnitude, we predict significant gain in the photoassociation rates into deeply bound levels of the excited state by a second pulse, red-detuned relative to the first one, and conveniently delayed.

We study off-resonant collective light scattering from ultracold atoms trapped in an optical lattice. Scattering from different atomic quantum states creates different quantum states of the scattered light, which can be distinguished by measurements of the spatial intensity distribution, quadrature variances, photon statistics, or spectral measurements. In particular, angle-resolved intensity measurements reflect global statistics of atoms (total number of radiating atoms) as well as local statistical quantities (single-site statistics even without optical access to a single site) and pair correlations between different sites. As a striking example we consider scattering from transversally illuminated atoms into an optical cavity mode. For the Mott-insulator state, similar to classical diffraction, the number of photons scattered into a cavity is zero due to destructive interference, while for the superfluid state it is nonzero and proportional to the number of atoms. Moreover, we demonstrate that light scattering into a standing-wave cavity has a nontrivial angle dependence, including the appearance of narrow features at angles, where classical diffraction predicts zero. The measurement procedure corresponds to the quantum nondemolition measurement of various atomic variables by observing light.

A self-trapped Bose-Einstein condensate is shown to be stabilized in two-dimensional free space by Rabi oscillations between two hyperfine states which make an effective interatomic interaction oscillate in time. The stabilization mechanism is elucidated by using a two-component Gross-Pitaevskii equation combined with a variational analysis. The parameter regime of stability is investigated.