A short-pulse photoexcitation of $1s\to 2s,2p$ transitions in the hydrogen atom is studied with perturbation theory and the finite-element method giving an almost exact solution of the time-dependent Schrodinger equation.

We present a multilevel theoretical approach to describe the behavior of a pulsed optically pumped (POP) ${}^{87}\mathrm{Rb}$ frequency standard based on a microwave cavity-vapor cell arrangement. The full Zeeman manifold of the ground-state hyperfine levels is then considered, and the dynamics induced among them by relaxation processes (buffer gas, spin exchange, and cell-walls collisions) is taken into account. The model includes as well the absorption of the pumping laser along the cell and the cavity feedback on the atoms; the effects related to a nonuniform excitation of the atomic sample are also discussed. Theoretical predictions are proven with a laboratory prototype of POP passive maser in which the clock transition is excited by means of the Ramsey technique. The agreement between theory and experiment is very satisfactory from both a quantitative and qualitative point of view, in terms of the shape of the Ramsey fringes, microwave power delivered by the atoms, and short-term frequency stability. In particular, a frequency stability of $1.2\times {10}^{-12}$ at one second has been measured, in very good agreement with the expected value. On this basis, the model has been extended to predict the short-term frequency stability of a POP frequency standard operating with optical detection. A shot-noise limited frequency stability (Allan deviation) of ${\sigma }_y\left(\tau \right)\approx 3\times {10}^{-14}{\tau }^{-1∕2}$ is foreseen. This value can be degraded by microwave phase noise and laser fluctuations so that the overall predicted clock stability is ${\sigma }_y\left(\tau \right)\approx 1.5\times {10}^{-13}{\tau }^{-1∕2}$.

We provide an in-depth analysis of the theory proposed by Holzmann, Chevallier, and Krauth (HCK) [Europhys. Lett. 82, 30001 (2008)] for predicting the temperature at which the Berezinskii-Kosterlitz-Thouless (BKT) transition to a superfluid state occurs in the harmonically trapped quasi-two-dimensional (2D) Bose gas. Their theory is based on a mean-field model of the system density, and we show that the HCK predictions change appreciably when an improved mean-field theory and identification of the transition point is used. In this analysis we develop a consistent theory that provides a lower bound for the BKT transition temperature in the trapped quasi-2D Bose gas.

The energy spectrum for three species of identical fermionic atoms close to a Feshbach resonance is computed by use of a nonperturbative flow equation. Already a simple truncation shows that for large scattering length $\mid a\mid$ the lowest energy state is a “trion” (or trimer) bound state of three atoms. At the location of the resonance, for $\mid a\mid \to \infty$, we find an infinite set of trimer bound states, with exponentially decreasing binding energy. This feature was pointed out by Efimov [V. Efimov, Phys. Lett. 33B, 563 (1970)]. It arises from limit cycle scaling, which also leads to a periodic dependence of the three body scattering coupling on $\ln \mid a\mid$. Extending our findings by continuity to nonzero density and temperature we find that a “trion phase” separates a Bose-Einstein condensate (BEC) and a BCS phase, with interesting quantum phase transitions for $T=0$.

It is shown theoretically how to directly obtain the energy distribution of a weakly interacting gas of bosons confined in an optical lattice in the tight-binding limit. This is accomplished by adding a linear potential to a suitably prepared lattice, and allowing the gas to evolve under the influence of the total potential. After a prescribed time, a spectral transform is effected where each (highly nonlocal) energy state is transformed into a distinct site of the lattice, thus allowing the energy distribution to be (nondestructively) imaged in real space. Evolving for twice the time returns the atoms to their initial state. The results suggest efficient methods to both measure the temperature in situ, as well as to cool atoms within the lattice: after applying the spectral transform one simply needs to remove atoms from all but a few lattice sites. Using exact numerical calculations, the effects of interactions and errors in the application of the lattice are examined.

We experimentally investigate the generation of high-order harmonics in a $4\text{−}\mathrm{mm}$-long gas cell using midinfrared femtosecond pulses at various wavelengths of $1240\mathrm{nm}$, $1500\mathrm{nm}$, and $1800\mathrm{nm}$. It is observed that the yield and cutoff energy of the generated high-order harmonics critically depend on focal position, gas pressure, and size of the input beam which can be controlled by an aperture placed in front of the focal lens. By optimizing the experimental parameters, we achieve a cutoff energy at $\sim 190\mathrm{eV}$ with the $1500\mathrm{nm}$ driving pulses, which is the highest for the three wavelengths chosen in our experiment.

We address the evolution of higher-order excited states, such as vortex and multihump solitons, in nonlocal media with synthetic, competing focusing and defocusing nonlinearities with different nonlocal transverse scales. We reveal that introduction of suitable competing effects makes possible the stabilization of vortex solitons with topological charge $m>2$, as well as one-dimensional multihump solitons with number of humps $p>4$, all of which are highly unstable in natural nonlocal materials with focusing nonlinearities.

The down-conversion dynamics of a single photon in a single three-level system are investigated theoretically. The wave functions of the output photons are obtained analytically as functions of the input photon profile, and the down-conversion probability is evaluated from these output wave functions. It is demonstrated that down-conversion of a single photon with unit efficiency is possible and the necessary conditions are clarified.

We describe a procedure for increasing the fractional delay (or delay-bandwidth product) of a slow-light system. A broadband input signal is sliced into several frequency bands. The light in each band propagates through a separate channel which possesses a highly reduced group velocity over a narrow frequency band. The output of each channel is then combined to form a single output field. For certain discretely distributed values of the group velocity of each channel, the output can replicate the input waveform without the need to adjust the output phase of each channel. Because this scheme makes use of many parallel channels, it can overcome a fundamental limit [D. A. B. Miller, Phys. Rev. Lett. 99, 203903 (2007)] to the delay-bandwidth product for single-channel devices. A practical design is proposed using spectral slicers and stimulated Brillouin scattering as the narrow-band slow-light process. Numerical simulation shows that such a channelized slow-light element can have nearly uniform gain and group index over very large bandwidths.

We demonstrate that buffer-gas cooling combined with laser ablation can be used to create coherent optical media with high optical depth and low Doppler broadening that offers metastable states with low collisional and motional decoherence. Demonstration of this generic technique opens pathways to coherent optics with a large variety of atoms and molecules. We use helium buffer gas to cool ${}^{87}\mathrm{Rb}$ atoms to below $7\mathrm{K}$ and slow atom diffusion to the walls. Electromagnetically induced transparency in this medium allows for 50% transmission in a medium with initial optical depth $D>70$ and for slow pulse propagation with large delay-bandwidth products. In the high-$D$ regime, we observe high-contrast spectrum oscillations due to efficient four-wave mixing.

We present a simple derivation of the formula for the Hamiltonian operator(s) that achieve the fastest possible unitary evolution between given initial and final states. We discuss how this formula is modified in pseudo-Hermitian quantum mechanics and provide an explicit expression for the most general optimal-speed quasi-Hermitian Hamiltonian. Our approach allows for an explicit description of the metric (inner product) dependence of the lower bound on the travel time and the universality (metric independence) of the upper bound on the speed of unitary evolutions.

We use the differential virial theorem (DVT) directly to display the approximate spatial dependence of the exchange-correlation (XC) force in He and Be, applying an exact integral constraint on the XC force, recently established by March and Nagy. In He, an analytic ground-state density $n\left(r\right)$, combined with the DVT plus the von Weizsäcker single-particle kinetic energy, suffices to determine an approximate XC force. For Be, the XC force is calculated for the semiempirical fine-tuned Hartree-Fock density, as proposed by Cordero et al. [Phys. Rev. A 75, 052502 (2007)]. However, for the single-particle kinetic energy, following Dawson and March, a phase $\theta \left(r\right)$ must be obtained by solving numerically a nonlinear pendulumlike equation.

We show that homodyne measurements can be used to demonstrate violations of Bell’s inequality with Gaussian states, when the local rotations used for these types of tests are implemented using nonlinear unitary operations. We reveal that the local structure of the Gaussian state under scrutiny is crucial in the performance of the test. The effects of finite detection efficiency are thoroughly studied and shown to only mildly affect the revelation of Bell violations. We speculate that our approach may be extended to other applications such as entanglement distillation where local operations are necessary elements besides quantum entanglement.

The question of a hidden variable interpretation of quantum contextuality in the Mermin-Peres square is considered. The Kochen-Specker theorem implies that quantum mechanics may be interpreted as a contextual hidden-variable theory. It is shown that such a hidden-variable description can be viewed as either contextual in the random variables mapping hidden states to observable outcomes or in the probability measure on the hidden state space. The latter view suggests that this apparent contextuality may be interpreted as a simple consequence of measurement disturbance, wherein the initial hidden state is altered through interaction with the measuring device, thereby giving rise to a possibly different final hidden-variable state from which the measurement outcome is obtained. In light of this observation, a less restrictive and, arguably, more reasonable definition of noncontextuality is suggested. To prove that such a description is possible, an explicit and, in this sense, noncontextual hidden-variable model is constructed, which reproduces all quantum theoretic predictions for the Mermin-Peres square. A critical analysis of some recent and proposed experimental tests of contextuality is also provided. Although the discussion is restricted to a four-dimensional Hilbert space, the approach and conclusions are expected to generalize to any Hilbert space.

We investigate Bose-Einstein condensation for ultracold bosonic atoms in two-dimensional systems. The functional renormalization group for the average action allows us to follow the effective interactions from molecular scales (microphysics) to the characteristic extension of the probe $l$ (macrophysics). In two dimensions the scale dependence of the dimensionless interaction strength $\lambda$ is logarithmic. Furthermore, for large $l$ the frequency dependence of the inverse propagator becomes quadratic. We find an upper bound for $\lambda$, and for large $\lambda$ substantial deviations from the Bogoliubov results for the condensate depletion, the dispersion relation and the sound velocity. The melting of the condensate above the critical temperature $T_c$ is associated to a phase transition of the Kosterlitz-Thouless type. The critical temperature in units of the density $T_c∕n$ vanishes for $l\to \infty$ logarithmically.

The effect of atomic position on the spontaneous emission and optical spectra of a three-level atom embedded in a photonic crystal was studied by considering the coherent two-band photonic-band-gap (PBG) reservoir. With the definite phase difference between the fields of the air band and dielectric band in this coherent PBG reservoir, we found that this coherent property grows stronger and results in the spectrum shift and the appearance of dark lines and kinks as the width of band gap gets smaller; and the variation of the atomic position leads to large shift of spectral peak. The averaged spectra of the system with an ensemble of atoms embedded in the dielectric region are blueshifted while those of atoms in the air region are redshifted. The spectra peaks can even shift more than 75% of the half width at half maximum. The feasible experimental systems composed of an ensemble of molecules (quantum dots or fluorescence dye) in photonic crystals are discussed.

We propose three criteria for identifying continuous variable entanglement between two many-particle systems with no restrictions on the quantum state of the local oscillators used in the measurements. Mistakenly asserting a coherent state for the local oscillator can lead to incorrectly identifying the presence of entanglement. We demonstrate this in simulations with 100 particles and also find that large number fluctuations do not prevent the observation of entanglement. Our results are important for quantum information experiments with realistic Bose-Einstein condensates or in optics with arbitrary photon states.

We present a joint experimental and theoretical study of spin depolarization in collisions of alkali-metal atoms with ${}^3\mathrm{He}$ in a magnetic field. A rigorous quantum theory for spin-changing transitions is developed and applied to calculate the spin exchange and spin relaxation rates of Li and K atoms in cryogenic ${}^3\mathrm{He}$ gas. Magnetic trapping experiments provide upper bounds to the spin exchange rates for $\mathrm{Li}\text{−}{}^3\mathrm{He}$ and $\mathrm{K}\text{−}{}^3\mathrm{He}$, which are in agreement with the present theory. Our calculations demonstrate that the alkali-metal atoms have extremely slow spin depolarization rates, suggesting a number of potential applications in precision spectroscopy and quantum optics.

We theoretically explore the generation of few-body analogs of fractional quantum Hall states. We consider an array of identical few-atom clusters $(n=2,3,4)$, each cluster trapped at the node of an optical lattice. By temporally varying the amplitude and phase of the trapping lasers, one can introduce a rotating deformation at each site. We analyze protocols for coherently transferring ground-state clusters into highly correlated states, producing theoretical fidelities (probability of reaching the target state) in excess of 99%.