We investigate the quantum electrodynamics of a single two-level atom located at the focus of a parabolic cavity. We first work out the modifications of the spontaneous emission induced by the presence of this boundary in the optical regime, where the dipole and the rotating-wave approximations apply. Furthermore, the single-photon state that leaves the cavity asymptotically is determined. The corresponding time-reversed single-photon quantum state is capable of exciting the atom in this extreme multimode scenario with near-unit probability. Using semiclassical methods, we derive a photon-path representation for the relevant transition amplitudes and show that it constitutes a satisfactory approximation for a wide range of wavelengths.

We study the creation of electron-positron pairs in the superposition of a nuclear Coulomb field and a two-color laser field of high intensity. Our focus lies on quantum interference effects, which may arise if the two laser frequencies are commensurable. We show that the interference manifests in the angular distributions of the created particles, which are discussed in the nuclear rest frame and the laboratory frame. Additionally, we demonstrate that the total pair-production rates can be affected by interference and identify the relative phase between the two laser modes, which optimizes the pair-production yield.

We introduce the concept of strong quantum speedup. We prove that approximating the ground-state energy of an instance of the time-independent Schrödinger equation, with $d$ degrees of freedom and large $d$, enjoys strong exponential quantum speedup. It can be easily solved on a quantum computer. Some researchers in discrete complexity theory believe that quantum computation is not effective for eigenvalue problems. One of our goals in this paper is to explain this dissonance.

We study the dynamics of spin-1 atoms in a periodic optical-lattice potential and an external magnetic field in a quantum quench scenario where we start from a superfluid ground state in a shallow lattice potential and suddenly raise the lattice depth. The time evolution of the nonequilibrium state shows collective collapse-and-revival oscillations of matter-wave coherence as well as oscillations in the spin populations. We show that the complex pattern of these two types of oscillations reveals details about the superfluid and magnetic properties of the initial many-body ground state. Furthermore, we show that the strengths of the spin-dependent and spin-independent atom-atom interactions can be deduced from the observations. The Hamiltonian that describes the physics of the final deep lattice not only contains two-body interactions but also effective multibody interactions, which arise due to virtual excitations to higher bands. We derive these effective spin-dependent three-body interaction parameters for spin-1 atoms and describe how spin mixing is affected. Spinor atoms are unique in the sense that multibody interactions are directly evident in the in situ number densities in addition to the momentum distributions. We treat both antiferromagnetic (e.g., ${}^{23}$Na) and ferromagnetic (e.g., ${}^{87}$Rb and ${}^{41}$K) condensates.

Frequency standards based on atomic states, such as Rb or Cs vapors, or single-trapped ions, are the most precise measures of time. Here we propose and analyze a precision oscillator approach based upon spins in a solid-state system, in particular, the nitrogen-vacancy defect in single-crystal diamond. We show that this system can have stability approaching portable atomic standards and is readily incorporable as a chip-scale device. Using a pulsed spin-echo technique, we anticipate an Allan deviation of ${\sigma }_y={10}^{-7}{\tau }^{-1/2}$ limited by thermally-induced strain variations; in the absence of such thermal fluctuations, the system is limited by spin dephasing and harbors an Allan deviation nearing $\sim {10}^{-12}{\tau }^{-1/2}$. Potential improvements based upon advanced diamond material processing, temperature stabilization, and nanophotonic engineering are discussed.

We characterize the frequency sensitivity of a cavity-stabilized laser to inertial forces and temperature fluctuations, and perform real-time feedforward to correct for these sources of noise. We measure the sensitivity of the cavity to linear accelerations, rotational accelerations, and rotational velocities by rotating it about three axes with accelerometers and gyroscopes positioned around the cavity. The worst-direction linear acceleration sensitivity of the cavity is $2\left(1\right)\times {10}^{-11}$ g${}^{-1}$ measured over 0–50 Hz, which is reduced by a factor of 50 to below ${10}^{-12}$ g${}^{-1}$ for low-frequency accelerations by real-time feedforward corrections of all of the aforementioned inertial forces. A similar idea is demonstrated in which laser frequency drift due to temperature fluctuations is reduced by a factor of 70 via real-time feedforward from a temperature sensor located on the outer wall of the cavity vacuum chamber.

The dynamics, appearing after a quantum quench, of a trapped, spin-orbit coupled, dilute atomic gas is studied. The characteristics of the evolution is greatly influenced by the symmetries of the system, and we especially compare evolution for an isotropic Rashba coupling and for an anisotropic spin-orbit coupling. As we make the spin-orbit coupling anisotropic, we break the rotational symmetry and the underlying classical model becomes chaotic; the quantum dynamics is affected accordingly. Within experimentally relevant time scales and parameters, the system thermalizes in a quantum sense. The corresponding equilibration time is found to agree with the Ehrenfest time, i.e., we numerically verify a $\sim \ln \left({\hslash }^{-1}\right)$ scaling. Upon thermalization, we find that the equilibrated distributions show examples of quantum scars distinguished by accumulation of atomic density for certain energies. At shorter time scales, we discuss nonadiabatic effects deriving from the spin-orbit-coupled induced Dirac point. In the vicinity of the Dirac point, spin fluctuations are large and, even at short times, a semiclassical analysis fails.

Since its discovery, the “ghost” diffraction phenomenon has emerged as an unconventional technique for optical imaging with very promising advantages. However, extracting the intensity and phase information of a structured and realistic object remains a challenge. Here we show that a ghost hologram can be recorded with a single-pixel configuration by adapting concepts from standard digital holography. The presented homodyne scheme enables phase imaging with nanometric depth resolution and three-dimensional focusing ability and shows a high signal-to-noise ratio.

Ultrafast dynamics of a molecular wave packet created by a strong 120-fs near-infrared (800 nm) laser pulse in iodine has been probed by synchronized 13.4-nm, 35-fs extreme-ultraviolet pulses delivered by the free-electron laser facility in Hamburg, FLASH. The kinetic energy release of the multiply charged ionic fragments reveals three essential steps of strong-field-induced molecular fragmentation dynamics: (i) The creation of I${}_2$${}^{2+}$ and (I${}_2$${}^{2+}$)${}^{*}$ molecular ions proceeds within (75 $\pm$ 15) fs full-width-at-half-maximum. (ii) With the onset of the I${}_2$${}^{2+}$ fragmentation the probability to lose a further electron within the same optical laser pulse rises with increasing I${}^{+}$—I${}^{+}$ internuclear separation and reaches its maximum after $\sim$30 fs with respect to the pulse maximum. (iii) Charge separation into the I${}_2$${}^{2+}\to {\mathrm{I}}^{2+}+\mathrm{I}$ dissociative channel with an asymmetric charge distribution is completed after (121 $\pm$ 22) fs.

Fermi gases with repulsive interactions are characterized by measuring their compressibility as a function of interaction strength. The compressibility is obtained from in-trap density distributions monitored by phase-contrast imaging. For interaction parameters $k_{F}a>0.25$, fast decay of the gas prevents the observation of equilibrium profiles. For smaller interaction parameters, the results are adequately described by first-order perturbation theory. We have developed a phase-contrast imaging method that compensates for dispersive distortions of the images.

We analyze the quench dynamics of a one-dimensional bosonic Mott insulator and focus on the time evolution of density correlations. For these we identify a pronounced propagation front, the velocity of which, once correctly extrapolated at large distances, can serve as a quantitative characteristic of the many-body Hamiltonian. In particular, the velocity allows the weakly interacting regime, which is qualitatively well described by free bosons, to be distinguished from the strongly interacting one, in which pairs of distinct quasiparticles dominate the dynamics. In order to describe the latter case analytically, we introduce a general approximation to solve the Bose-Hubbard Hamiltonian based on the Jordan-Wigner fermionization of auxiliary particles. This approach can also be used to determine the ground-state properties. As a complement to the fermionization approach, we derive explicitly the time-dependent many-body state in the noninteracting limit and compare our results to numerical simulations in the whole range of interactions of the Bose-Hubbard model.

In this work we investigate a generic method able to extract information on molecular organization in biological samples from polarized second harmonic generation (SHG) microscopy, without the need to infer an a priori model for the molecular orientational distribution. The mean orientation of this distribution, as well as its first and third orders of symmetry, are estimated by monitoring SHG intensity signals under a varying incident polarization. We introduce, in particular, a reduction of the problem to a two-dimensional approach appropriate to the microscopy geometry. This method allows us to retrieve determining information which is not available in the traditional model-oriented methods, as illustrated in molecular-order imaging in collagen fibrils. The precision of the parameters estimation is evaluated by a Monte Carlo analysis, based on the Poisson noise statistics of the measured signal.

We propose a general method by which experiments on ultracold gases can be used to determine the topological properties of the energy bands of optical lattices, as represented by the map of the Berry curvature across the Brillouin zone. The Berry curvature modifies the semiclassical dynamics and hence the trajectory of a wave packet undergoing Bloch oscillations. However, in two dimensions these trajectories may be complicated Lissajous-like figures, making it difficult to extract the effects of Berry curvature in general. We propose how this can be done using a “time-reversal” protocol. This compares the velocity of a wave packet under positive and negative external force, and allows a clean measurement of the Berry curvature over the Brillouin zone. We discuss how this protocol may be implemented and explore the semiclassical dynamics for three specific systems: the asymmetric hexagonal lattice and two “optical flux” lattices in which the Chern number is nonzero. Finally, we discuss general experimental considerations for observing Berry curvature effects in ultracold gases.

We have used the narrow $2S_{1/2}\to 3P_{3/2}$ transition in the ultraviolet (uv) to laser cool and magneto-optically trap (MOT) ${}^6$Li atoms. Laser cooling of lithium is usually performed on the $2S_{1/2}\to 2P_{3/2}$ (D2) transition, and temperatures of $\sim$300 $\mu$K are typically achieved. The linewidth of the uv transition is seven times narrower than the D2 line, resulting in lower laser cooling temperatures. We demonstrate that a MOT operating on the uv transition reaches temperatures as low as 59 $\mu$K. Furthermore, we find that the light shift of the uv transition in an optical dipole trap at 1070 nm is small and blueshifted, facilitating efficient loading from the uv MOT. Evaporative cooling of a two spin-state mixture of ${}^6$Li in the optical trap produces a quantum degenerate Fermi gas with $3\times {10}^6$ atoms in a total cycle time of only 11 s.

We report the laser cooling and trapping of neutral potassium on an open transition. Fermionic ${}^{40}$K is captured using a magneto-optical trap (MOT) on the closed $4S_{1/2}\to 4P_{3/2}$ transition at 767 nm and then transferred, with high efficiency, to a MOT on the open $4S_{1/2}\to 5P_{3/2}$ transition at 405 nm. Because the $5P_{3/2}$ state has a smaller linewidth than the $4P_{3/2}$ state, the Doppler limit is reduced from 145 μK to 24 μK, and we observe temperatures as low as 63(6) $\mu$K. The density of trapped atoms also increases, due to reduced temperature and reduced expulsive light forces. We measure a two-body loss coefficient of $\beta =1.4\left(1\right)\times {10}^{-10}$ cm${}^3$/s near saturation intensity, and estimate an upper bound of $8\times {10}^{-18}$ cm${}^2$ for the ionization cross section of the $5P$ state at 405 nm. The combined temperature and density improvement in the 405 nm MOT is a twenty-fold increase in phase-space density over our 767 nm MOT, showing enhanced precooling for quantum gas experiments. A qualitatively similar enhancement is observed in a 405 nm MOT of bosonic ${}^{41}$K.

The $R$-matrix incorporating time (RMT) method is a method developed recently for solving the time-dependent Schrödinger equation for multielectron atomic systems exposed to intense short-pulse laser light. We have employed the RMT method to investigate the time delay in the photoemission of an electron liberated from a $2p$ orbital in a neon atom with respect to one released from a $2s$ orbital following absorption of an attosecond xuv pulse. Time delays due to xuv pulses in the range 76–105 eV are presented. For an xuv pulse at the experimentally relevant energy of 105.2 eV, we calculate the time delay to be $10.2\pm 1.3$ attoseconds (as), somewhat larger than estimated by other theoretical calculations, but still a factor of 2 smaller than experiment. We repeated the calculation for a photon energy of 89.8 eV with a larger basis set capable of modeling correlated-electron dynamics within the neon atom and the residual Ne${}^{+}$ ion. A time delay of $14.5\pm 1.5$ as was observed, compared to a $16.7\pm 1.5$ as result using a single-configuration representation of the residual Ne${}^{+}$ ion.

A procedure is discussed for creating coherent superpositions of motional states of ion strings. The motional states are across the structural transition linear-zigzag, and their coherent superposition is achieved by means of spin-dependent forces, such that a coherent superposition of the electronic states of one ion evolves into an entangled state between the chain's internal and external degrees of freedom. It is shown that the creation of such an entangled state can be revealed by performing Ramsey interferometry with one ion of the chain.

We show experimentally and numerically that free-electron-laser (FEL) oscillators behave in a very similar way to conventional actively-mode-locked lasers. This stems from the similar structures of their underlying Haus equations. A comparative study of the temporal evolutions of the pulse train shapes and spatiotemporal regimes is performed on a Nd:YVO${}_4$ laser and a storage-ring free-electron laser. Furthermore, since direct observations of time-resolved pulse shapes and spectra are more accessible on free-electron lasers, the analogy also potentially enables one to investigate mode-locked laser dynamics using existing FEL facilities.

The possibility of controlled direct laser-nuclear excitations is considered from a quantum control perspective. The controllability of laser-driven electric dipole and magnetic dipole transitions among pure nuclear states is analyzed. Within a set of realistic and general conditions, atomic nuclei are demonstrated to possess full state controllability. Additionally, an analysis of the nuclear state excitation probability as a function of the laser control field is conducted. This control landscape is shown to possess a generic topology, which has important physical consequences for achieving optimal nuclear state excitation with laser fields. Last, an assessment is given of the technological challenges that need to be considered when implementing direct nuclear control in the laboratory.

Mutually coupled modes of a pair of active LRC circuits, one with amplification and another with an equivalent amount of attenuation, provide an experimental realization of a wide class of systems where gain and loss mechanisms break the Hermiticity while preserving parity-time $\mathcal{PT}$ symmetry. For a value ${\gamma }_{\mathcal{PT}}$ of the gain and loss strength parameter the eigenfrequencies undergo a spontaneous phase transition from real to complex values, while the normal modes coalesce, acquiring a definite chirality. The consequences of the phase transition in the spatiotemporal energy evolution are also presented.