Cold circular Rydberg atoms are produced and magnetically trapped. The trap is characterized by direct spatial imaging of ion distributions, ion counting, and state-selective field ionization. At room temperature, we observe about 70% of the trapped atoms remaining after 6 ms. We measure a trap oscillation frequency increase of the circular Rydberg atom trap relative to the ground-state atom trap due to the larger magnetic moment of the circular Rydberg atoms. Simulations of the center-of-mass and internal-state evolution of circular states in our magnetic trap are performed and results are in good agreement with experimental observations.

The violation of a Bell inequality certifies the presence of entanglement even if neither party trusts their measurement devices. Recently Moroder et al. [T. Moroder, J.-D. Bancal, Y.-C. Liang, M. Hofmann, and O. Gühne, Phys. Rev. Lett. 111, 030501 (2013)] showed how to make this statement quantitative, using semidefinite programming to calculate how much entanglement is certified by a given violation. Here I adapt their techniques to the case in which Bob's measurement devices are in fact trusted, the setting for Einstein-Podolsky-Rosen steering inequalities. Interestingly, all of the steering inequalities studied turn out to require negativity for their violations. This supports a significant strengthening of Peres's conjecture that negativity is required to violate a bipartite Bell inequality.

We develop a general theoretical framework for the analytical description of the interaction of a model diatomic molecular system with an intense, arbitrarily polarized monochromatic laser field. The model molecule comprises an electron in the field of two zero-range potentials separated by the internuclear distance. This model has an exact analytical solution within the theoretical framework of the quasistationary quasienergy (Floquet) approach. In addition to the development of this general framework, we also present a detailed analysis of the weak-field limit, within which we obtain both the frequency-dependent polarizability and the angle-resolved photodetachment cross section for the model system. These fundamental properties are analyzed for both homonuclear and heteronuclear molecular systems in a linearly polarized laser field, for both ground and excited electronic states, and for arbitrary orientation of the molecular axis relative to the polarization vector of the laser field. The analytical expressions for the polarizability and angle-resolved photoelectron spectra exhibit characteristic double-slit interference patterns, allowing one to study their dependence on the parameters of the problem beyond the level of the Born approximation.

We present a theoretical and experimental study aimed at characterizing statistical regimes in a random laser. Both the theoretical simulations and the experimental results show the possibility of three regions of fluctuations increasing the pumping energy. An initial Gaussian regime is followed by Lévy statistics, and Gaussian statistics is recovered again for high pump pulse energy. These different statistical regimes are possible in a weakly diffusive active medium, while the region of Lévy statistics disappears when the medium is strongly diffusive presenting always a Gaussian regime with smooth emission spectrum. Experiments and theory agree in identification of the key parameters determining the statistical regimes of the random laser.

We construct optimal time-local control pulses based on a multipartite entanglement measure as target functional. The underlying control Hamiltonians are derived in a purely algebraic fashion, and the resulting pulses drive a composite quantum system rapidly into that highly entangled state which can be created most efficiently for a given interaction mechanism, and which bears entanglement that is robust against decoherence. Moreover, it is shown that the control scheme is insensitive to experimental imperfections in first order.

We report a detailed investigation on the properties of intensity correlation spectra for laser beams interacting with cold atoms under the condition of electromagnetically induced transparency (EIT). We describe the transition of their intensity fluctuations from correlation to anticorrelation as the mean intensity of the fields increases. Such a transition occurs for laser frequencies around the EIT resonance, which is characterized by a correlation peak. The transition point between correlation and anticorrelation is independent of power broadening and provides directly the ground-state coherence time. We introduce a method to extract in real time the correlation spectra of the system. The experiments were done in two distinct magneto-optical traps, one for cesium and the other for rubidium atoms, employing different detection schemes. A simplified theory is introduced assuming three-level atoms in $\Lambda$ configuration interacting with a laser with stochastic phase fluctuations, providing a good agreement with the experimental observations.

The calculation of the fundamental limits of nonlinear susceptibilities posits that when a quantum system has a nonlinear response at the fundamental limit, only three energy eigenstates contribute to the first and second hyperpolarizability. This is called the three-level ansatz and is the only unproven assumption in the theory of fundamental limits. In light of the observation that the measured nonlinear response of a majority of molecules falls far short of these limits, the three-level ansatz warrants closer scrutiny. All calculations that are based on direct solution of the Schrödinger equation, including systems of arbitrarily placed electrons and nuclei in external electromagnetic fields and interacting electrons in an arbitrary potential, whose configuration space is sampled using numerical optimization techniques, yield intrinsic hyperpolarizabilities less than 0.709 and intrinsic second hyperpolarizabilities less than 0.6. In this work, we show that relaxing the three-level ansatz and allowing an arbitrary number of states to contribute leads to divergence of the optimized intrinsic hyperpolarizability in the limit of an infinite number of states, what we call the many-state catastrophe. This is not surprising given that the divergent systems are most likely not derivable from the Schrödinger equation, yet obey the sum rules. The sums rules are the second ingredient in limit theory and apply also to systems with more general Hamiltonians. These “exotic Hamiltonians” may not model any real systems found in nature. Indeed, a class of transition moments and energies that come form the sum rules do not have a corresponding Hamiltonian that is expressible in differential form. In this work, we show that the three-level ansatz acts as a constraint that excludes many of the nonphysical Hamiltonians and prevents the intrinsic hyperpolarizability from diverging. We argue that this implies that the true fundamental limit is smaller than previously calculated. Since the three-level ansatz does not lead to the largest possible nonlinear response, contrary to its assertion, we propose the intriguing possibility that the three-level ansatz is true for any system that obeys the Schrödinger equation, yet this assertion may be unprovable.

We construct a theory for long-distance quantum communication based on sharing entanglement through a linear chain of $N$ elementary swapping segments of length $L=Nl$ where $l$ is the length of each elementary swap setup. Entanglement swapping is achieved by linear optics, photon counting, and postselection, and we include effects due to multiphoton sources, transmission loss, and detector inefficiencies and dark counts. Specifically we calculate the resultant four-mode state shared by the two parties at the two ends of the chain, and we derive the two-photon coincidence rate expected for this state and thereby the visibility of this long-range-entangled state. The expression is a nested sum with each sum extending from zero to infinite photons, and we solve the case $N=2$ exactly for the ideal case (zero dark counts, unit-efficiency detectors, and no transmission loss) and numerically for $N=2$ in the nonideal case with truncation at $n_{\max }=3$ photons in each mode. For the general case, we show that the computational complexity for the numerical solution is $n_{\max }^{12N}$.

We have investigated magnetically tunable Feshbach resonances arising from the interaction of Li(${}^{2}S$) with metastable Yb(${}^3{P}_2$) and (${}^3{P}_0$). For Yb(${}^3{P}_2$), all the resonance features are strongly suppressed by inelastic collisions that produce Yb in its lower-lying ${}^3{P}_1$ and ${}^3{P}_0$ states. For Yb(${}^3{P}_0$), sharp resonances exist but they are extremely narrow (widths less than 1 mG).

Boson-fermion pair correlations in a mixture are considered at zero temperature in the $T$-matrix approximation. Special attention is paid to the Luttinger theorem. In a strict random-phase approximation variant of the Nozières-Schmitt-Rink approach, it is shown that this theorem is respected also in the homogeneous infinite matter case. We calculate the corresponding occupation numbers of fermions and bosons and the condensate depletion. We also show that in the limit of very small boson density, our results are in good agreement with the results found in the literature for the Fermi polaron in strongly imbalanced Fermi-Fermi mixtures.

By Bernoulli's law, an increase in the relative speed of a fluid around a body is accompanied by a decrease in the pressure. Therefore, a rotating body in a fluid stream experiences a force perpendicular to the motion of the fluid because of the unequal relative speed of the fluid across its surface. It is well known that light has a constant speed irrespective of the relative motion. Does a rotating body immersed in a stream of photons experience a Bernoulli-like force? We show that, indeed, a rotating dielectric cylinder experiences such a lateral force from an electromagnetic wave. In fact, the sign of the lateral force is the same as that of the fluid-mechanical analog as long as the electric susceptibility is positive ($\epsilon >{\epsilon }_0$), but for negative-susceptibility materials (e.g., metals) we show that the lateral force is in the opposite direction. Because these results are derived from a classical electromagnetic scattering problem, Mie-resonance enhancements that occur in other scattering phenomena also enhance the lateral force.

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.