We demonstrate an atom trap geometry for ${}^{87}$Rb which is capable of producing ultrahigh atom densities. Reradiation forces, which usually limit high densities, can be avoided in dark spontaneous-force optical traps (dark SPOTs) by sheltering atoms from intense trapping light. Here we demonstrate a dynamic implementation of a dark SPOT, resulting in an increase in atom density by almost two orders of magnitude up to $1.3\times {10}^{12}$ cm${}^{-3}$. Holographic control of the trapping beams and dynamic switching between magneto-optical trap (MOT) and dark SPOT configuration allows us to optimize the trapping geometry. We have identified the ideal size of the dark core to be six times larger than the MOT. Our method also avoids unwanted heating so that we reach a record phase-space density for a MOT.

The $s$-wave interaction is usually the dominant form of interactions in atomic Bose-Einstein condensates (BECs). Recently, Feshbach resonances have been employed to reduce the strength of the $s$-wave interaction in many atomic species. This opens the possibilities to study magnetic dipole-dipole interactions (MDDIs) in BECs, where the novel physics resulting from long-range and anisotropic dipolar interactions can be explored. Using a variational method, we study the effect of MDDIs on the statics and dynamics of atomic BECs with tunable $s$-wave interactions for a variety of species, including both nonalkali metals with large magnetic dipole moments (${}^{52}$Cr, ${}^{164}$Dy, ${}^{168}$Er) and alkali metals (with much smaller magnetic dipole moments). A parameter of magnetic Feshbach resonances, ${\epsilon }_{dd,\text{max}}$, is used to quantitatively indicate the feasibility of experimentally observing MDDI effects in different atomic species. We find that strong MDDI effects should be observable in both in-trap and time-of-flight behaviors, not only for the strongly magnetic dipolar species but also for the alkali-metal BECs of ${}^7$Li, ${}^{39}$K, and ${}^{133}$Cs. In addition, we predict several effects which should be experimentally observable. Our results provide a helpful guide for experimentalists to realize and study atomic dipolar quantum gases.

We present an ultrahigh-sensitivity gravimeter based on an ${}^{87}$Rb atom interferometer using stimulated Raman transitions. Compared with our previous work, a two-dimensional magneto-optical trap is added in the new gravimeter to increase the atom number and improve the detection signal-to-noise ratio, and a better optical phase-locked loop system is used to reduce the phase noise of Raman beams. Benefiting from these efforts and the excellent performance of the active vibration isolator, a short-term sensitivity of about 4.2 $\mu \text{Gal}/\sqrt{\text{Hz}}$ ($1\mu \mathrm{Gal}=1\times {10}^{-8}$ $\text{m}/{\text{s}}^2$) is reached, which improves the sensitivity by a factor of 2 compared with the former best reported value. By a modulation experiment, we further indicate that the residual vibration noise contribution is about 1.2 $\mu \text{Gal}/\sqrt{\text{Hz}}$, which implies a possible improvement over the present absolute gravity measurement level by about one order of magnitude. Moreover, we demonstrate a calibration experiment to directly evaluate the sub-$\mu$Gal resolution of our gravimeter.

We present a theoretical study of the collective optical effects which can occur in groups of three and four quantum dots. We define conditions for stable subradiant (dark) states, rapidly decaying super-radiant states, and spontaneous trapping of excitation. Each quantum dot is treated like a two-level system. The quantum dots are, however, realistic, meaning that they may have different transition energies and dipole moments. The dots interact via a short-range coupling which allows excitation transfer across the dots, but conserves the total population of the system. We calculate the time evolution of single-exciton and biexciton states using the Lindblad equation. In the steady state the individual populations of each dot may have permanent oscillations with frequencies given by the energy separation between the subradiant eigenstates.

We introduce sum-frequency generation (SFG) as a physical detector for high-power two-mode squeezed coherent states with arbitrary frequency separation, as produced by parametric oscillators above threshold. Using a formalism of collective modes, we describe both two-mode squeezing and degenerate squeezing on equal footing and derive simple relations between the input degree of squeezing and the measured SFG quadrature noise. We show that the SFG quadratures provide a direct measure of the input squeezing and discuss the sensitivity limits of the proposed method.

We introduce the concept of spatial spectral phase gradient, and demonstrate, both theoretically and experimentally, how this concept could be employed for generating single- and multipath self-accelerating beams. In particular, we show that the trajectories of the accelerating beams are determined a priori by different key spatial frequencies through direct spectrum-to-distance mapping. In the nonparaxial regime, our results clearly illustrate the breakup of Airy beams from a different perspective, and demonstrate how circular, elliptic, or hyperbolic accelerating beams can be created by judiciously engineering the spectral phase. Furthermore, we found that the accelerating beams still follow the predicted trajectory also for vectorial wave fronts. Our approach not only generalizes the idea of Fourier-space beam engineering along arbitrary convex trajectories, but also offers possibilities for beam or pulse manipulation not achievable through standard direct real-space approaches or by way of time-domain phase modulation.

We propose to thermalize a low-dimensional photon gas and obtain photonic Bose-Einstein condensation by optomechanical interactions in a microscopic optical cavity, with a single longitudinal mode and many transverse modes. The geometry of the short cavity is such that it provides a low-frequency cutoff at a photonic energy far above the thermal energy, so that thermal emission of photons is suppressed and the photon number is conserved. While previous experiments on photonic Bose-Einstein condensation have used dye molecules for photon gas thermalization, we here investigate thermalization owing to interactions with thermally fluctuating nanomechanical oscillators forming the cavity mirrors. In the quantum degenerate regime, the nanomechanical cavity converts broadband optical radiation into tuneable coherent radiation.

We analyze the phase-conjugate coupling of a pair of optomechanical oscillator modes driven by the time-dependent beat note of a two-color optical field. The dynamics of the direct and phase-conjugate modes exhibit familiar time-reversed qualities, leading to opposite sign temperatures for the modes in the classical regime of operation. These features are limited by quantum effects due to the noncommutative nature of quantum-mechanical operators. The effects are measurable by readout of the oscillator via a qubit. As a potential application of this system in sensing, we discuss a protocol applying phase-conjugate swaps to cancel or reduce external forces on the system.

It is known that it is possible to encode a logical qubit over many physical qubits such that it is immune to the effects of collective decoherence, and it is possible to perform universal quantum computation using these “decoherence-free” qubits. However, current proposed methods of performing gates on these encoded qubits could be difficult to implement, or could take too much time to perform. Here we investigate whether exploiting ring exchange interactions, which may be naturally present, can simplify the implementation of these gates in any way. Using a ring exchange interaction, we have found a way to create a controlled-Z gate on the four-qubit decoherence-free subspace and the three-qubit decoherence-free subsystem using a sequence with five pulses. This could be useful in situations where simplicity is important or where ring exchange interactions are prominent. We also investigate how timing errors and magnetic field fluctuations affect the fidelity of this gate.

The hyperfine interaction constants of the $2p^4{(}^{3}P)3p$ ${}^2{D}_{3/2,5/2}^o$, ${}^4{D}_{1/2-7/2}^o$, and ${}^4{P}_{1/2-5/2}^o$ levels in neutral fluorine are investigated theoretically. Large-scale calculations are carried out using the multiconfiguration Hartree-Fock (MCHF) and Dirac-Hartree-Fock (MCDHF) methods. In the framework of the MCHF approach, the relativistic effects are taken into account in the Breit-Pauli approximation using nonrelativistic orbitals. In the fully relativistic approach, the orbitals are optimized using the Dirac-Coulomb Hamiltonian with correlation models inspired by the nonrelativistic calculations. Higher-order excitations are captured through multireference configuration interaction calculations including the Breit interaction. In a third (intermediate) approach, the Dirac-Coulomb-Breit Hamiltonian matrix is diagonalized in a relativistic configuration space built with nonrelativistic MCHF radial functions converted into Dirac spinors using the Pauli approximation. The magnetic dipole hyperfine-structure constants calculated with the three relativistic models are consistent and reveal unexpectedly large effects of relativity for ${}^2{D}_{5/2}^o$, ${}^4{P}_{3/2}^o$, and ${}^4{P}_{5/2}^o$. The agreement with the few available experimental values is satisfactory. The strong $J$ dependence of relativistic corrections on the hyperfine constants is investigated through the detailed analysis of the orbital, spin-dipole, and contact relative contributions calculated with the nonrelativistic magnetic dipole operator.

Collinear laser spectroscopy was performed on an atomic beam of stable ${}^{55}$Mn. An ion beam of ${}^{55}$Mn${}^{+}$ was generated in an ion source, accelerated to 15 keV, and neutralized via charge-exchange reactions with a Na vapor. A long-lived metastable state of Mn i, near-resonantly populated in the charge-exchange process, was investigated via laser probing in addition to a laser excitation from the ground state in Mn i. The relative population of the Mn i metastable state compared to that of the ground state was found to be $0.7\pm 0.3$. A theoretical calculation, which included feeding to the ground state and the metastable state from higher-energy excited electronic states populated in the charge-exchange process, agreed with the present result. The deduced $A$ and $B$ hyperfine coupling constants agreed with literature values, where available.

In this paper, an apparatus for measuring electron-scattering cross sections while applying a strong axial magnetic field is described. The first original experiment performed with this setup is the measurement of the total cross sections for pyrimidine (1,3-diazine), which are presented for the incident electron energy range of 8–500 eV. Generally good agreement with earlier theoretical predictions is found after accounting for the angular acceptance (angular resolution for forward scattering) of the apparatus.

By considering photoionization of the C${}_{60}$ fullerene, we elucidate the contributions of various classical and quantum physics phenomena appearing in this process. By comparing the results, based on the ab initio and model approaches, we map the well-resolved features of the photoabsorption spectrum to single-particle and collective excitations which have a different physical nature. It is demonstrated that the peculiarities arising in the photoionization spectrum of C${}_{60}$ atop the dominating plasmon excitations have a quantum origin. In particular, we demonstrate that a series of individual peaks can be assigned either to the optically allowed discrete transitions or to the ionization of particular molecular orbitals of the system. The analysis performed gives detailed information on the nature of numerous features in the photoabsorption spectrum of C${}_{60}$.

We describe an experiment in which cold rubidium atoms, confined in an elongated magnetic trap, are excited by transverse oscillation of the trap center. The temperature after excitation exhibits resonance as a function of the driving frequency. We measure these resonances at several different trap frequencies. In order to interpret the experiments, we develop a simple model that incorporates both collisions between atoms and the anharmonicity of the real three-dimensional trapping potential. As well as providing a precise connection between the transverse harmonic oscillation frequency and the temperature resonance frequency, this model gives insight into the heating and loss mechanisms and into the dynamics of driven clouds of cold trapped atoms.

Motivated by compelling advances in manipulating cold Rydberg (Ry) atoms in optical traps, we consider the effect of the large extent of a Ry electron wave function on trapping potentials. We find that, when the Ry orbit lies outside inflection points in the laser intensity landscape, the atom can stably reside in laser intensity maxima. Effectively, the free-electron ac polarizability of the Ry electron is modulated by the intensity landscape and can accept both positive and negative values. We apply these insights to determining the magic wavelengths for Ry-ground-state transitions for alkali-metal atoms trapped in infrared optical lattices. We find magic wavelengths to be around $10\mu \mathrm{m}$ with exact values that depend on Ry-state quantum numbers.

We propose and analyze a scheme to entangle the collective spin states of two spatially separated bimodal Bose-Einstein condensates. Using a four-mode approximation for the atomic field, we show that elastic collisions in a state-dependent potential simultaneously create spin-squeezing in each condensate and entangle the collective spins of the two condensates. We investigate mostly analytically the nonlocal quantum correlations that arise in this system at short times and show that Einstein-Podolsky-Rosen (EPR) entanglement is generated between the condensates. At long times we point out macroscopic entangled states and explain their structure. The scheme can be implemented with condensates in state-dependent microwave potentials on an atom chip.

We consider the quasiparticle excitations of a trapped dipolar Bose-Einstein condensate. By mapping these excitations onto linear and angular momentum we show that the roton modes are clearly revealed as discrete fingers in parameter space, whereas the other modes form a smooth surface. We examine the properties of the roton modes and characterize how they change with the dipole interaction strength. We demonstrate how the application of a perturbing potential can be used to engineer angular rotons, i.e., allowing us to controllably select modes of nonzero projection of angular momentum to become the lowest energy rotons.

We theoretically analyze the pairing instability of a three-dimensional ultracold atomic Fermi gas towards a Fulde-Ferrell superfluid, in the presence of Rashba spin-orbit coupling and in-plane Zeeman field. We use the standard Thouless criterion for the onset of superfluidity, with which the effect of pair fluctuations is partially taken into account by approximately using a mean-field chemical potential at zero temperature. This gives rise to an improved prediction of the superfluid transition temperature beyond mean field, particularly in the strong-coupling unitary limit. We also investigate the pairing instability with increasing Rashba spin-orbit coupling, along the crossover from a Bardeen-Cooper-Schrieffer superfluid to a Bose-Einstein condensate of rashbons (i.e., the tightly bound state of two fermions formed by strong Rashba spin-orbit coupling).

In a two-component condensate, a vortex in one of the components will induce a density modulation in the other component. This density modulation is centered at the location of the vortex core and can take the form of a peak or trough in density. As such the total density is nonzero and the system is referred to as a “coreless vortex.” In this paper we give an analytical form, based on a variational calculation, for the coreless vortex in a miscible homogeneous condensate. In particular we can calculate the density of the coreless vortex at its core, the associated length scales, and the energetic instability of a multicharged coreless vortex.

The nonlinear phenomenon of four-wave mixing (FWM) is investigated using a method, where, without the need of calculus, both phase and amplitudes of the mixing fields are visualized simultaneously, giving a complete overview of the FWM dynamics. This is done by introducing a set of Stokes-like coordinates of the electric fields, which reduce the FWM dynamics to a closed two-dimensional surface, similar to the Bloch sphere of quantum electrodynamics or the Pointcaré sphere in polarization dynamics. The coordinates are chosen so as to use the gauge invariance symmetries of the FWM equations which also give the conservation of action flux known as the Manley-Rowe relations. This reduces the dynamics of FWM to the one-dimensional intersection between the closed two-dimensional surface and the phase-plane given by the conserved Hamiltonian. The analysis is advantageous for visualizing phase-dependent FWM phenomena which are found in a large variety of nonlinear systems and even in various optical communication schemes.