Using $\epsilon$ expansion technique proposed by Nishida and Son [Phys. Rev. Lett. 97, 050403 (2006)] we derive an effective Lagrangian (Ginzburg-Landau-type functional) of the degenerate unitary Fermi gas to the next-to-leading order in $\epsilon$. It is demonstrated that for many realistic situations it is sufficient to retain leading order terms in the derivative expansion. The functional is used to study vortex structure in the symmetric gas, and interface between normal and superfluid phases in the polarized gas. Typical vortex size, $r_0{k}_F=0.92$, where $k_F$ is Fermi momentum, agrees well with results of previous work [A. Bulgac and Y. Yu, Phys. Rev. Lett. 91, 190404 (2003)]. Surface free energy is about 3 times larger than the value previously quoted in the literature.

We study sequential scattering in superradiance from a Bose-Einstein condensate pumped by a two-frequency laser beam. We find that the distribution of atomic side modes presents highly different patterns for various frequency difference between the two pump components. These observations reveal that the frequency overlap between the end-fire modes related to different side modes plays an essential role in the dynamics of sequential superradiant scattering. The numerical results from a semiclassical model qualitatively agree with our observations.

The realization of negative refraction in atomic gases requires a strong magnetic response of the atoms. Current proposals for such systems achieve a parametric enhancement of the magnetic response by one inverse power of the fine-structure constant $\alpha$, but still rely on high gas densities. To enable further enhancement, here we study in detail the magnetic and electric response to a probe field interacting with three-level atoms in ladder configuration. In our first model, the three transitions are driven by a control field and the electric and magnetic components of the probe field, giving rise to a closed interaction loop. In a reference model, the coherent driving is replaced by an incoherent pump field. A time-dependent analysis of the closed-loop system enables us to identify the different contributions to the medium response and to determine the enhancement mechanism. Based on these results, we show that in addition to the parametric enhancement of ${\alpha }^{-1}\sim 137$, our system allows for a further nonparametric enhancement of the magnetic response by almost two orders of magnitude, relaxing the requirement for a high vapor density.

In this paper, we present a study of depolarization of a supercontinuum across its spectral range as a function of the femtosecond laser pump intensity for an anisotropic crystalline condensed medium, potassium-dihydrogen-phosphate (KDP) crystal, and compare our results with commonly used supercontinuum generation (SCG) materials, namely borosilicate glass Schott (BK-7) glass (representing isotropic amorphous condensed media) and $\mathrm{Ba}{\mathrm{F}}_2$ (isotropic crystalline condensed media). Our results show that at higher input powers, depolarization in the continuum increases for BK-7, $\mathrm{Ba}{\mathrm{F}}_2$, and along the direction of the optic axis of the KDP crystal. However, in the case of KDP crystal, we observe that the depolarization properties are strongly dependent on (i) the plane of polarization of incident light and (ii) the orientation of the crystal with respect to the incident light. Our studies also confirm that one can achieve SCG in a KDP crystal that maintains the same state of input polarization even at high input intensities when proper orientation of the crystal is used.

Electron-impact ionization cross sections for ${\mathrm{Li}}_2$ and $\mathrm{Li}_2{}^{+}$ are calculated using a configuration-average distorted-wave method. Bound orbitals for the molecule and its ions are calculated using a single-configuration self-consistent-field method based on a linear combination of Slater-type orbitals. The bound orbitals are transformed onto a two-dimensional lattice $(r,\theta )$, which is variable in the radial coordinate and constant in the angular coordinate, from which Hartree with local exchange potentials are constructed. The single-particle Schrödinger equation is then solved for continuum distorted waves with $S$-matrix boundary conditions. Total ionization cross sections for ${\mathrm{Li}}_2$ at an equilibrium internuclear separation of $R=5.0\mathrm{a.u.}$ and for $\mathrm{Li}_2{}^{+}$ at an equilibrium internuclear separation of $R=5.9\mathrm{a.u.}$ are presented.

We report two-channel calculations for $e^{\pm }\text{−}{\mathrm{H}}_2$ scattering ($X{}^1\Sigma _g^{+}\to X{}^1\Sigma _g^{+}$,$B{}^3\Sigma _u^{+}$ for electrons and $X{}^1\Sigma _g^{+}\to X{}^1\Sigma _g^{+},B{}^1\Sigma _u^{+}$ for positrons). We provide independent estimates of the electron ${}^2\Sigma _g^{+}$ Feshbach resonance (though for a limited range of interatomic distances) in good agreement with benchmark calculations [D. T. Stibbe and J. Tennyson, J. Phys. B 31, 815 (1998)]. Resonance enhanced vibrational excitation cross sections were obtained with a time-dependent local complex potential approach and compare favorably with recent calculations [R. Celiberto et al., Phys. Rev. A 77, 012714 (2008)] and experimental data. The time resolution also provides good physical insight into the transient dynamics. In a previous work, we predicted the existence of a positron-hydrogen ${}^2\Sigma _g^{+}$ Feshbach resonance based on a fixed-nuclei scattering calculation (equilibrium geometry) that was not observed experimentally [J. P. Sullivan et al., J. Phys. B 34, L467 (2001)]. We further investigate the resonance potential in this study and our results indicate that the ${}^2\Sigma _g^{+}$ potential crosses the $B{}^1\Sigma _u^{+}$ state just above the equilibrium interatomic distance of the ground state, giving rise to a short-lived transient. Though the positronium formation channel could also play a role, the state crossing sheds light on the controversy between theory and experiment.

It is shown that the discrete energies of a scattering Hamiltonian calculated under the influence of an artificial confining potential can be used to determine its phase shifts. Two potentials that have the same energy under the influence of the confining potential have exactly the same phase shift at that energy when the confining potential is removed. Thus the phase shifts of a complicated many-body problem can be extracted by solving the Schrödinger equation under the influence of the confining potential, and then making reference to the energies and phase shifts of a much simpler model potential calculated in the same confining potential. Calculations on real systems gave very precise phase shifts for the $e^{-}\text{−}\mathrm{H}$ and $e^{-}\text{−}\mathrm{He}$ systems.

Using a simple scheme based on nondegenerate four-wave mixing in a hot vapor, we generate bright twin beams which display a quantum noise reduction in the intensity difference of more than $8\mathrm{dB}$. The absence of a cavity makes the system immune to external perturbations, and strong quantum noise reduction is observed at frequencies as low as $4.5\mathrm{kHz}$ and over a large frequency range.

We consider the coherent stimulated Raman process developing in an optically dense disordered atomic medium, which can also incoherently scatter the light over all outward directions. The Raman process is discussed in the context of a quantum memory scheme and we point out the difference in its physical nature from a similar but not identical protocol based on the effect of electromagnetically induced transparency (EIT). We show that the Raman and EIT memory schemes do not compete but complement one another and each of them has certain advantages in the area of its applicability. We include in our consideration an analysis of the transient processes associated with switching the control pulse off or on and follow how they modify the probe pulse dynamics on the retrieval stage of the memory protocol.

The recoil effects of spontaneous photon emissions during optical pumping of a trapped three-level atom are exactly calculated. Without resort to the Lamb-Dicke approximation, and considering arbitrary detuning and saturation of the pump laser, the density of recoil shifts in phase space is derived. It is shown that this density is not of Gaussian shape, and that it becomes isotropic in phase space only for a branching ratio corresponding to fluorescence scattering but unfavorable for optical pumping. The dependence of its anisotropy on the laser saturation is discussed in the resonant case, and the mapping of moments of the atom’s center-of-mass motion due to the pumping is presented. Moreover, it is shown how optimum parameters for protecting the center-of-mass quantum state from pump-induced disturbance depend on the specific property to be protected.

We study undistinguishable two-species Bose-Einstein condensates (BECs) trapped in double wells. In the mean-field approximation we map the quantum system into a classical model and investigate the existence and stability of the fixed point solutions. By appropriately varying the amplitude of the high-frequency periodic modulation on the energy bias between the two wells, we tune the tunneling strength in the adiabatic Rosen-Zener type effectively. Starting from two typical initial states, we study the evolution of the system and find that the interspecies interaction can produce totally distinct results, which is expected to provide a route to manipulate the BEC distribution.

We develop practical schemes for the measurement of the covariance matrix for intrinsic angular-momentum variables in quantum optics. We particularize this approach to two-beam polarimetry and interferometry, as well as to ensembles of two-level atoms interacting with classical fields. We show the practical advantages of noisy simultaneous measurements.

The fractional Fourier transform (FRFT) naturally exists in strongly nonlocal nonlinear (SNN) media and the propagation of optical beams in SNN media can be simply regarded as a self-induced FRFT. Through the FRFT technique the evolution of fields in SNN media can be conveniently dealt with, and an arbitrary square-integrable input field presents itself generally as a revivable higher-order spatial soliton which reconstructs its profile periodically after every four Fourier transforms. The self-induced FRFT illuminates the prospects for SNN media in new applications such as continuously tunable nonlinearity-induced FRFT devices.

Barash has calculated the Casimir forces between parallel birefringent plates with optical axes parallel to the plate boundaries [Izv. Vyssh. Uchebn. Zaved., Radiofiz. 12, 1637 (1978)]. The interesting feature of the solution compared to the case of isotropic plates is the existence of a Casimir torque which acts to line up the optical axes if they are not parallel or perpendicular. The forces were found from a calculation of the Helmholtz free energy of the electromagnetic field. Given the length of the calculations in this problem and hopes of an experimental measurement of the torque, it is important to check the results for the Casimir forces by a different method. We provide this check by calculating the electromagnetic stress tensor between the plates and showing that the resulting forces are in agreement with those found by Barash.

We study sets of pure states in a Hilbert space of dimension $d$ which are mutually unbiased (MU), that is, the moduli of their scalar products are equal to zero, one, or $1∕\sqrt{d}$. Each of these sets will be called a MU constellation, and if four MU bases were to exist for $d=6$, they would give rise to 35 different MU constellations. Using a numerical minimization procedure, we are able to identify only 18 of them in spite of extensive searches. The missing MU constellations provide the strongest numerical evidence so far that no seven MU bases exist in dimension 6.

We investigate blackbody-induced energy shifts for low-lying levels of atomic systems, with a special emphasis on transitions used in current and planned high-precision experiments on atomic hydrogen and ionized helium. Fine-structure- and Lamb-shift-induced blackbody shifts are found to increase with the square of the nuclear charge number, whereas blackbody shifts due to virtual transitions decrease with increasing nuclear charge as the fourth power of the nuclear charge. We also investigate the decay width acquired by the ground state of atomic hydrogen, due to interaction with blackbody photons. The corresponding width is due to an instability against excitation to higher excited atomic levels, and due to blackbody-induced ionization. These effects limit the lifetime of even the most fundamental, a priori absolutely stable, “asymptotic” state of atomic theory, namely, the ground state of atomic hydrogen.

We study the dependence of the ac Stark shifts of electronic energies on the molecular orientation relative to the polarization direction of an incident intense laser field, using a three-dimensional non-Hermitian Floquet method and $\mathrm{H}_2{}^{+}$ as a model system. Simultaneously, we also study the orientation-dependent high-order harmonic generation (HHG) and multiphoton ionization (MPI). We find that with the presence of near-one-photon resonance, the Stark effect strongly mixes electronic states of different symmetries to create quasienergy states (QESs). The orientation dependence of multiphoton processes, in which these QESs play an important role, becomes complex. Population transfer is better achieved with aligned molecules and optimized orientation. When the energies of emitted photons are lower than the ionization energy, the Stark effect plays an important role in the orientation dependence of HHG intensity and polarization. It also is important for MPI, when the Keldysh parameter is larger than 1. Results from fixed-nuclei calculations for a series of internuclear distances are used to obtain values for different vibrational states. With a multiphoton resonance, the HHG intensity of the fixed-nuclei model resembles that of the lowest vibrational state. Molecular vibration of $\mathrm{H}_2{}^{+}$ has a great effect in MPI and the off-resonant HHG.

We investigated the complex index of refraction in the x-ray regime of atoms in laser light. The laser (intensity up to ${10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$, wavelength $800\mathrm{nm}$) modifies the atomic states but, by assumption, does not excite or ionize the atoms in their electronic ground state. Using quantum electrodynamics, we devise an ab initio theory to calculate the dynamic dipole polarizability and the photoabsorption cross section, which are subsequently used to determine the real and imaginary part, respectively, of the refractive index. The interaction with the laser is treated nonperturbatively; the x-ray interaction is described in terms of a one-photon process. We numerically solve the resolvents involved using a single-vector Lanczos algorithm. Finally, we formulate rate equations to copropagate a laser and an x-ray pulse through a gas cell. Our theory is applied to argon. We study the x-ray polarizability and absorption near the argon $K$ edge over a large range of dressing-laser intensities. We find electromagnetically induced transparency (EIT) for x rays on the Ar $1s\to 4p$ pre-edge resonance. We demonstrate that EIT in Ar allows one to imprint the shape of an ultrafast laser pulse on a broader x-ray pulse (duration $100\mathrm{ps}$, photon energy $3.2\mathrm{keV}$). Our work thus opens new opportunities for research with hard x-ray sources.

We performed an experimental and theoretical investigation of Ramsey-type spectroscopy in conjunction with high-order-harmonic generation. The ninth harmonic $(\lambda \simeq 88\mathrm{nm})$ of a femtosecond Ti:sapphire laser was used to excite a pair of autoionizing states of krypton. The outcome of the ionization process, detected by an ion-mass spectrometer, shows the characteristic quantum interference pattern. The behavior of the fringe contrast was interpreted on the basis of a simple analytical model, which reproduced well the experimental results without any free parameter.

The ionization rate of molecules in intense laser fields may be much lower than that of atoms with similar binding energy. This phenomenon is termed the ionization suppression of molecules and is caused by the molecular inner structure. In this paper, we perform a comprehensive study of the ionization suppression of homonuclear diatomic molecules in intense laser fields of linear and circular polarizations. We find that for linear polarization the total ionization rate and the ionization suppression depend greatly on the molecular alignment, and that for circular polarization the ionization suppression of molecules in the antibonding (bonding) shells disappears (appears) for laser intensities around ${10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$. We also find that the molecular photoelectron energy spectra are greatly changed by the interference effect, even though the total ionization rate of molecules remains almost the same as that of their companion atoms.