It has long been known that particles with short-range repulsive interactions in spatial dimension $d=1$ form universal quantum liquids in the low density limit: all properties can be related to those of the spinless free Fermi gas. Previous renormalization-group (RG) analyses demonstrated that this universality is described by a RG fixed point, infrared stable for $d<2$, of the zero density gas. We show that for $d>2$ the same fixed point describes the universal properties of particles with short-range attractive interactions near a Feshbach resonance; the fixed point is now infrared unstable, and the relevant perturbation is the detuning of the resonance. Some exponents are determined exactly, and the same expansion in powers of $(d-2)$ applies for scaling functions for $d<2$ and $d>2$. A separate exact RG analysis of a field theory of the particles coupled to “molecules” finds an alternative description of the same fixed point, with identical exponents; this approach yields a $(4-d)$ expansion which agrees with the recent results of Nishida and Son [Phys. Rev. Lett. 97, 050403 (2006)]. The existence of the RG fixed point implies a universal phase diagram as a function of density, temperature, population imbalance, and detuning; in particular, this applies to the crossover between the Bose-Einstein condensate (BEC) and Bardeen-Cooper-Schrieffer (BCS) superfluid of $s$-wave paired fermions. Our results open the way towards computation of these universal properties using the standard field-theoretic techniques of critical phenomena, along with a systematic analysis of corrections to universality. We also propose a $1∕N$ expansion [based upon models with $\mathrm{Sp}\left(2N\right)$ symmetry] of the fixed point and its vicinity, and use it to obtain results for the phase diagram.

We present an ab initio quantum investigation of the high-order harmonic generation (HHG) cutoff extension using intense few-cycle chirped laser pulses. For a few-cycle chirped driving laser pulse, it is shown that significant cutoff extension can be achieved through the optimization of the chirping rate parameters. The HHG power spectrum is calculated by solving accurately and efficiently the time-dependent Schrödinger equation by means of the time-dependent generalized pseudospectral method. The time-frequency characteristics of the HHG power spectrum are analyzed in detail by means of the wavelet transform of the time-dependent induced dipole acceleration. In addition, we perform classical trajectory simulation of the strong-field electron dynamics and electron return map. It is found that the quantum and classical results provide complementary and consistent information regarding the underlying mechanisms responsible for the substantial extension of the cutoff region.

An experimental and theoretical investigation is made of the angular spectrum of a near-resonant femtosecond laser pulse propagating through sodium vapor. A directional fluorescence emission corresponding to single-photon sodium transition $3S\to 3P_{1∕2,3∕2}$ has been registered for the pump wavelength ranging from $540\text{to}605\mathrm{nm}$. It is found that such emission can be detected under the conditions of single-photon (enhanced by two-photon) resonance of pump frequency with relevant atomic states. Theoretical treatment of the field-matter interaction by means of the nonperturbative (semiclassical) approach revealed conical components of the cylindrically symmetric beam spectrum originating both from the fluorescence induced by coherent atomic polarization and four-wave mixing.

We theoretically demonstrate the optimization of field-free molecular alignment by phase-shaped femtosecond laser pulses. The effect is assessed in ${\mathrm{O}}_2$ at $T=60\mathrm{K}$ under realistic conditions of intensity and pulse shaping. The spectral laser phase is sampled through 128 control parameters and a self-learning evolutionary algorithm combined with a nonperturbative regime calculation is used in order to design the specific phase that maximizes the degree of alignment. The postpulse molecular alignment appears significantly enhanced compared to a Fourier-transform-limited pulse of same energy. The analysis of the target state reveals that the solution is close to the optimal one.

Fourier transform is an essential ingredient in Shor’s factoring algorithm. In the standard quantum circuit model with the gate set {$\mathbb{U}\left(2\right)$, controlled-NOT}, the discrete Fourier transforms $F_N={\left({\omega }^{ij}\right)}_{N\times N}$, $i,j=0,1,\dots ,N-1$, $\omega =e^{2\pi i∕N}$, can be realized exactly by quantum circuits of size $O\left(n^2\right)$, $n=\ln N$, and so can the discrete sine or cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci $(2+1)$-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms $F_N$ and the discrete sine or cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that an approximation is unavoidable in the implementation of Fourier transforms by braiding conformal blocks.

The hyperfine structure of the $4s{}^{2}S_{1∕2}\text{−}3d{}^{2}S_{5∕2}$ quadrupole transition at $729\mathrm{nm}$ in ${}^{43}\mathrm{Ca}^{+}$ has been investigated by laser spectroscopy using a single trapped ${}^{43}\mathrm{Ca}^{+}$ ion. We determine the hyperfine structure constants of the metastable level as $A_{D_{5∕2}}=3.8931\left(2\right)\mathrm{MHz}$ and $B_{D_{5∕2}}=4.241\left(4\right)\mathrm{MHz}$. The isotope shift of the transition with respect to ${}^{40}\mathrm{Ca}^{+}$ was measured to be ${\Delta }_{\mathrm{iso}}^{43,40}=4134.713\left(5\right)\mathrm{MHz}$. We demonstrate the existence of transitions that become independent of the first-order Zeeman shift at nonzero low magnetic fields. These transitions might be better suited for building a frequency standard than the well-known “clock transitions” between $m=0$ levels at zero magnetic field.

In recent articles [K. Mishima et al., Phys. Rev. A, 66, 033401 (2002); S. D. Chao, Phys. Rev. A, 72, 053414 (2005)] it was proposed to use the residue theorem for the exact calculation of the transition amplitude describing strong-field ionization of atomic systems within Keldysh theory. This should avoid the necessity of applying the method of steepest descent (saddle-point approximation). Comparing the results of both approaches for atomic hydrogen a difference by a factor of 2 was found for the $1s$ and an even more drastic deviation for the $2s$ state. Thus it was concluded that the use of the saddle-point approximation is problematic. In this work the deviations are explained and it is shown that the previous conclusion is based on an unjustified neglect of an important contribution occurring in the application of the residue theorem. Furthermore, the applicability of the method of steepest descent for the ionization of Rydberg states is discussed and an improvement of the standard result is suggested that successfully removes the otherwise drastic failure for large principal quantum numbers.

Coherent population transfer in a laser-driven four-level system in a tripod configuration is experimentally investigated with a rare-earth-metal-ion-doped crystal $({\mathrm{Pr}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5)$. The population transfers observed here indicate that a main process inducing them is not optical pumping, which is an incoherent process inducing population transfer. Moreover, numerical simulation, which well reproduces the experimental results, also shows that the process inducing the observed population transfers is similar to stimulated Raman adiabatic passage (STIRAP) in the sense that this process possesses characteristic features of STIRAP.

When the parameters of a physical system are varied, the eigenvalues of observables can undergo crossings and avoided crossings among themselves. It is relevant to be aware of such points since important physical processes often occur there. In a recent paper [M. Bhattacharya and C. Raman, Phys. Rev. Lett. 97, 140405 (2006)] we introduced a powerful algebraic solution to the problem of finding (avoided) crossings in atomic and molecular spectra. This was done via a mapping to the problem of locating the roots of a polynomial in the parameters of interest. In this article we describe our method in detail. Given a physical system that can be represented by a matrix, we show how to find a bound on the number of (avoided) crossings in its spectrum, the scaling of this bound with the size of the Hilbert space and the parametric dependencies of the Hamiltonian, the interval in which the (avoided) crossings all lie in parameter space, the number of crossings at any given parameter value, and the minimum separation between the (avoided) crossings. We also show how the crossings can reveal the symmetries of the physical system, how (avoided) crossings can always be found without solving for the eigenvalues, how they may sometimes be found even in case the Hamiltonian is not fully known, and how crossings may be visualized in a more direct way than displayed by the spectrum. In the accompanying paper [M. Bhattacharya and C. Raman, Phys. Rev. A 75, 033406 (2007)] we detail the application of these techniques to atoms and molecules.

A number of interesting phenomena occur at points where the energy levels of an atom or a molecule (anti) cross as a function of some parameter such as an external field. In a previous paper [M. Bhattacharya and C. Raman, Phys. Rev. Lett. 97, 140405 (2006)] we have outlined powerful mathematical techniques useful in identifying the parameter values at which such (avoided) crossings occur. In the accompanying article [M. Bhattacharya and C. Raman, Phys. Rev A 75, 033405 (2007)] we have developed the mathematical basis of these algebraic techniques in some detail. In this article we apply these level-crossing methods to the spectra of atoms and molecules in a magnetic field. In the case of atoms the final result is the derivation of a class of invariants of the Breit-Rabi Hamiltonian of magnetic resonance. These invariants completely describe the parametric symmetries of the Hamiltonian. In the case of molecules we present an indicator which can tell when the Born-Oppenheimer approximation breaks down without using any information about the molecular potentials other than the fact that they are real. We frame our discussion in the context of Feshbach resonances in the atom-pair ${}^{23}\mathrm{Na}\text{−}{}^{85}\mathrm{Rb}$ which are of current interest.

We consider the properties of a gas of bosonic diatomic molecules in the limit when few of the molecules are dissociated. Taking into account the effects of dissociation and scattering among molecules and atoms, we calculate the dispersion relation for a molecule, and the thermal depletion of the condensate. We calculate the dependence of the Bose-Einstein-condensation (BEC) temperature of a uniform gas on the atom-atom scattering length, and conclude that, for a broad Feshbach resonance, the condensation temperature increases as the molecular state becomes less strongly bound, thereby giving rise to a maximum in the transition temperature in the BEC-BCS crossover. We also argue on general grounds that, for a gas in a harmonic trap and for a narrow Feshbach resonance, the condensation temperature will decrease with increasing scattering length.

We investigate the effects of long-ranged dipole-dipole potential on the transition temperature of a weakly interacting Bose gas. We apply the two-fluid model to derive the energy spectra of the thermal and the condensate parts. From the interaction modified spectra of the system, the formula for the shift of transition temperature was derived. Compared to the conventional weakly interacting Bose system with contact potential only where thermal effect is larger, we find that the condensate effect is about two times that of the thermal part in the dipolar system. Due to the relative smallness of dipole-dipole interaction with respect to the contact interaction in current dipolar Bose-Einstein condensation, we suggest to measure the dipolar effect by tuning the scattering length to negligible small by the Feshbach resonance technique.

The deceleration of beams of neutral particles possessing an electron spin with time-dependent inhomogeneous magnetic fields is demonstrated experimentally. Half the kinetic energy of a velocity-selected part of a pulsed supersonic beam of hydrogen atoms in the ground state is removed using six pulsed magnetic field stages.

Entanglement distribution between trapped-atom quantum memories, viz. single atoms in optical cavities, is addressed. In most scenarios, the rate of entanglement distribution depends on the efficiency with which the state of traveling single photons can be transferred to trapped atoms. This loading efficiency is analytically studied for two-level, $V$-level, $\Lambda$-level, and double-$\Lambda$-level atomic configurations by means of a system-reservoir approach. An off-resonant nonadiabatic approach to loading $\Lambda$-level trapped-atom memories is proposed, and the ensuing trade-offs between the atom-light coupling rate and input photon bandwidth for achieving a high loading probability are identified. The nonadiabatic approach allows a broad class of optical sources to be used, and in some cases it provides a higher system throughput than what can be achieved by adiabatic loading mechanisms. The analysis is extended to the case of two double-$\Lambda$ trapped-atom memories illuminated by a polarization-entangled biphoton.

We report experimental results on mixed-state generation by multiple scattering of polarization-entangled photon pairs created from parametric down-conversion. By using a large variety of scattering optical systems we have experimentally obtained entangled mixed states that lie upon and below the Werner curve in the linear entropy-tangle plane. We have also introduced a simple phenomenological model built on the analogy between classical polarization optics and quantum maps. Theoretical predictions from such a model are in full agreement with our experimental findings.

A simple and efficient quantum-nondemolition measurement (QND) scheme is proposed in which the arrival of a signal photon is detected without affecting the qubit state. The proposed QND scheme functions even if the ancillary photon is replaced with weak light composed of vacuum and one-photon states. Although the detection scheme is designed for entanglement sharing applications, it is also suitable for general purification of a single-photon state.

We show that adiabatic evolution of a low-dimensional lattice of quantum spins with a spectral gap can be simulated efficiently. In particular, we show that as long as the spectral gap $\Delta E$ between the ground state and the first excited state is any constant independent of $n$, the total number of spins, then the ground-state expectation values of local operators, such as correlation functions, can be computed using polynomial space and time resources. Our results also imply that the local ground-state properties of any two spin models in the same quantum phase can be efficiently obtained from each other. A consequence of these results is that adiabatic quantum algorithms can be simulated efficiently if the spectral gap does not scale with $n$. The simulation method we describe takes place in the Heisenberg picture and does not make use of the finitely correlated state–matrix product state formalism.

Atomic hydrogen provides a unique test case for computational electronic structure methods, since its electronic excitation energies are known analytically. With only one electron, hydrogen contains no electronic correlation and is therefore particularly susceptible to spurious self-interaction errors introduced by certain computational methods. In this paper we focus on many-body perturbation theory (MBPT) in Hedin’s $GW$ approximation. While the Hartree-Fock and the exact MBPT self-energy are free of self-interaction, the correlation part of the $GW$ self-energy does not have this property. Here we use atomic hydrogen as a benchmark system for $GW$ and show that the self-interaction part of the $GW$ self-energy, while nonzero, is small. The effect of calculating the $GW$ self-energy from exact wave functions and eigenvalues, as distinct from those from the local-density approximation, is also illuminating.

Photoionization spectra have been recorded in the $4s$, $4p$, and $3d$ resonance regions for the Kr I isoelectronic sequence using both the dual laser produced plasma (DLP) technique (at DCU) to produce photoabsorption spectra, and the merged ion beam and synchrotron radiation technique (at ASTRID) to measure absolute photoionization cross sections. Profile parameters are compared for the $4s\text{−}np$ resonances of ${\mathrm{Rb}}^{+}$ and ${\mathrm{Sr}}^{2+}$. Many $4p\to ns$, $md$ transitions are identified with the aid of Hartree-Fock calculations, and consistent quantum defects are observed for the various $ns$ and $md$ Rydberg series. Absolute single and double photoionization cross sections recorded in the $3d$ region for ${\mathrm{Rb}}^{+}$ and ${\mathrm{Sr}}^{2+}$ ions show preferential decay via double photoionization. This is only the second report to our knowledge where both the DLP technique and the merged-beam technique have been used simultaneously to record photoionization spectra, and the advantages of both techniques (i.e., better resolution in the case of DLP and values for absolute photoionization cross sections in the case of the merged-beam technique) are highlighted.

We use perturbation theory to directly calculate the van der Waals and dipole-dipole energy shifts of pairs of interacting Rb Rydberg atoms for different quantum numbers $n$, $\ell$, $j$, and $m_j$, taking into account a large number of perturbing states. Our results can be used to identify good experimental parameters and illuminate important considerations for applications of the “Rydberg-excitation blockade.” We also use the results of the calculation to explain features of previous experimental data on the Rydberg-excitation blockade. To explore control methods for the blockade, we discuss energy shifts due to atom-atom interaction in an external electric field.