We propose a scheme for optimal Gaussian purification of coherent states from several imperfect copies. The proposal is experimentally demonstrated for the case of two copies of a coherent state sent through independent noisy channels. Our purification protocol relies on only linear optics and an ancilla vacuum state, rendering this approach an interesting alternative to the more complex protocols of entanglement distillation and quantum error correction.

Highly sensitive, nondestructive, real-time spectroscopic determination of the two-dimensional kinetic momentum distribution of a cold-atom sample is performed with the three-beam measurement of the recoil-induced resonances. The measurements performed with an operating magneto-optical trap reveal slow velocity drifts within a stationary atomic cloud and strong anisotropy and asymmetry of the non-Maxwellian momentum distribution. The developed method can be easily extended to three dimensions.

We study various measures of classicality of the states of open quantum systems subject to decoherence. Classical states are expected to be stable in spite of decoherence, and are thought to leave conspicuous imprints on the environment. Here these expected features of environment-induced superselection are quantified using four different criteria: predictability sieve (which selects states that produce least entropy), purification time (which looks for states that are the easiest to find out from the imprint they leave on the environment), efficiency threshold (which finds states that can be deduced from measurements on a smallest fraction of the environment), and purity loss time (that looks for states for which it takes the longest to lose a set fraction of their initial purity). We show that when pointer states—the most predictable states of an open quantum system selected by the predictability sieve—are well defined, all four criteria agree that they are indeed the most classical states. We illustrate this with two examples: an underdamped harmonic oscillator, for which coherent states are unanimously chosen by all criteria, and a free particle undergoing quantum Brownian motion, for which most criteria select almost identical Gaussian states (although, in this case, the predictability sieve does not select well defined pointer states).

We calculate the one- and two-loop corrections of order $\alpha {\left(Z\alpha \right)}^6$ and ${\alpha }^2{\left(Z\alpha \right)}^6$, respectively, to the Lamb shift in hydrogenlike systems using the formalism of nonrelativistic quantum electrodynamics. We obtain general results valid for all hydrogenic states with nonvanishing orbital angular momentum and for the normalized difference of $S$ states. These results involve the expectation value of local effective operators and relativistic corrections to Bethe logarithms. The one-loop correction is in agreement with previous calculations for the particular cases of $S$, $P$, and $D$ states. The two-loop correction in the order ${\alpha }^2{\left(Z\alpha \right)}^6$ includes the pure two-loop self-energy and all diagrams with closed fermion loops. The obtained results allow one to obtain improved theoretical predictions for all excited hydrogenic states.

A method to approximate transmission probabilities for a nonseparable multidimensional barrier is applied to a waveguide model. The method uses complex barrier-crossing orbits to represent reaction probabilities in phase space and is uniform in the sense that it applies at and above a threshold energy at which classical reaction switches on. Above this threshold the geometry of the classically reacting region of phase space is clearly reflected in the quantum representation. Two versions of the approximation are applied. A harmonic version which uses dynamics linearized around an instanton orbit is valid only near threshold but is easy to use. A more accurate and more widely applicable version using nonlinear dynamics is also described.

We report an experimental demonstration of the three-dimensional orientation of gas-phase molecules by applying the combination of an electrostatic and an elliptically polarized laser field. Three-dimensional orientation was verified using a technique in which two-dimensional ion imaging and time-of-flight mass spectrometry are complementarily used.

Both the trapping geometry and the interatomic interaction strength of a dilute ultracold fermionic gas can be well controlled experimentally. Adapting the interaction strength between the fermionic atoms allows tuning the gas from a molecular condensate to a Bardeen-Cooper-Schrieffer superfluid. We adopt a functional integral point of view to investigate how the superfluid properties vary during this crossover. In particular, the critical superfluid velocity for flowing through an optical lattice is derived. The observation of undamped motion in an optical lattice constitutes a hallmark of superfluidity, also in the fermionic systems. We discuss our theoretical results for the critical velocity of a fermionic superfluid in comparison to the experimental results for a bosonic superfluid in an optical lattice.

We report the implementation of Grover’s quantum search algorithm in the scalable system of trapped atomic ion quantum bits. Any one of four possible states of a two-qubit memory is marked, and following a single query of the search space, the marked element is successfully recovered with an average probability of 60(2)%. This exceeds the performance of any possible classical search algorithm, which can only succeed with a maximum average probability of 50%.

We propose an interferometric method to investigate the nonlocality of high-dimensional two-photon orbital angular momentum states generated by spontaneous parametric down conversion. We incorporate two half-integer spiral phase plates and a variable-reflectivity output beam splitter into a Mach-Zehnder interferometer to build an orbital angular momentum analyzer. This setup enables testing the nonlocality of high-dimensional two-photon states by repeated use of the Clauser-Horne-Shimony-Holt inequality.

We derive an approximate expression for a “radiative potential” which can be used to calculate QED strong Coulomb field radiative corrections to energies and electric dipole $\left(E1\right)$ transition amplitudes in many-electron atoms with an accuracy of a few percent. The expectation value of the radiative potential gives radiative corrections to the energies. Radiative corrections to $E1$ amplitudes can be expressed in terms of the radiative potential and its energy derivative (the low-energy theorem): the relative magnitude of the radiative potential contribution is $\sim {\alpha }^3{Z}^2\ln (1∕{\alpha }^2{Z}^2)$, while the sum of other QED contributions is $\sim {\alpha }^3(Z_i+1{)}^2$, where $Z_i$ is the ion charge; that is, for neutral atoms $(Z_i=0)$ the radiative potential contribution exceeds other contributions $\sim Z^2$ times. The advantage of the radiative potential method is that it is very simple and can be easily incorporated into many-body theory approaches: relativistic Hartree-Fock, configuration interaction, many-body perturbation theory, etc. As an application we have calculated the radiative corrections to the energy levels and $E1$ amplitudes as well as their contributions ($-0.34\%$ and $+0.43\%$, respectively) to the parity nonconserving (PNC) $6s$-$7s$ amplitude in neutral cesium $(Z=55)$. Combining these results with the QED correction to the weak matrix elements $(-0.41\%)$ we obtain the total QED correction to the PNC $6s$-$7s$ amplitude, $(-0.32\pm 0.03)\%$. The cesium weak charge $Q_W=-72.66\left(29{)}_{\exp }\right(36{)}_{\mathrm{theor}}$ agrees with the Standard Model value $Q_W^{\mathrm{SM}}=-73.19\left(13\right)$, the difference is 0.53(48).

Joint quantum measurements of noncommuting observables are possible, if one accepts an increase in the measured variances. A necessary condition for a joint measurement to be possible is that a joint probability distribution exists for the measurement. This fact suggests that there may be a link with Bell inequalities, as these will be satisfied if and only if a joint probability distribution for all involved observables exists. We investigate the connections between Bell inequalities and conditions for joint quantum measurements to be possible. Mermin’s inequality for the three-particle Greenberger-Horne-Zeilinger state turns out to be equivalent to the condition for a joint measurement on two out of the three quantum systems to exist. Gisin’s Bell inequality for three coplanar measurement directions, meanwhile, is shown to be less strict than the condition for the corresponding joint measurement.

Fault-tolerant logical operations for qubits encoded by Calderbank-Shor-Steane codes are discussed, with emphasis on methods that apply to codes of high rate, encoding $k$ qubits per block with $k>1$. It is shown that the logical qubits within a given block can be prepared by a single recovery operation in any state whose stabilizer generator separates into $X$ and $Z$ parts. Optimized methods to move logical qubits around and to achieve controlled-NOT and Toffoli gates are discussed. It is found that the number of time steps required to complete a fault-tolerant quantum computation is the same when $k>1$ as when $k=1$.

We study the eigenlevel spectrum of quantum adiabatic algorithm for 3-satisfiability problem, focusing on single-solution instances. The properties of the ground state and the associated gap, crucial for determining the running time of the algorithm, are found to be far from the predictions of random matrix theory. The distribution of gaps between the ground and the first excited state shows an abundance of small gaps. Eigenstates from the central part of the spectrum are, on the other hand, well described by random matrix theory.

The optimal creation of a targeted unitary transformation $W$ is considered under the influence of an external control field. The controlled dynamics produces the unitary transformation $U$ and the goal is to seek a control field that minimizes the cost $J=\parallel W-U\parallel$. The optimal control landscape is the cost $J$ as a functional of the control field. For a controllable quantum system with $N$ states and without restrictions placed on the controls, the optimal control landscape is shown to have extrema with $N+1$ possible distinct values, where the desired transformation at $U=W$ is a minimum and the maximum value is at $U=-W$. The other distinct $N-1$ extrema values of $J$ are saddle points. The results of this analysis have significance for the practical construction of unitary transformations.

The configuration interaction in many-electron atoms may cause anomalies in the fine structure which make the intervals small and very sensitive to variation of the fine-structure constant. Repeated precision measurements of these intervals over a long period of time can put strong constraints on possible time variation of the fine-structure constant. We consider the $5p^4{}^{3}P_{2,1,0}$ fine-structure multiplet in the ground state of neutral tellurium as an example. Here the effect of change of the fine structure constant is enhanced about 100 times in the relative change of the small energy interval between the ${}^{3}P_1$ and ${}^{3}P_0$ states.

We theoretically investigate the effects of laser polarization on the photoelectron angular distribution through laser-induced continuum structure. We focus on a polarization geometry where the probe and dressing lasers are both linearly polarized and change the relative polarization angle between them. We find that the total ionization yield and the branching ratio into different ionization channels change as a function of the relative polarization angle, and accordingly the photoelectron angular distribution is altered. We present specific results for the $4p_{1∕2}\text{−}6p_{1∕2}$ and $4p_{3∕2}\text{−}6p_{3∕2}$ systems of the K atom and show that the change of the polarization angle leads to a significant modification of the photoelectron angular distribution.

We present a detailed study of the spatial self-organization of laser-driven atoms in an optical cavity, an effect predicted on the basis of numerical simulations [P. Domokos and H. Ritsch, Phys. Rev. Lett. 89, 253003 (2002)] and observed experimentally [A. T. Black et al., Phys. Rev. Lett. 91, 203001 (2003)]. Above a threshold in the driving laser intensity, from a uniform distribution the atoms evolve into one of two stable patterns that produce superradiant scattering into the cavity. We derive analytic formulas for the threshold and critical exponent of this phase transition from a mean-field approach. Numerical simulations of the microscopic dynamics reveal that, on a laboratory time scale, a hysteresis masks the mean-field behavior. Simple physical arguments explain this phenomenon and provide analytical expressions for the observable threshold. Above a certain density of the atoms a limited number of “defects” appear in the organized phase and influence the statistical properties of the system. The scaling of the cavity cooling mechanism and the phase-space density with the atom number is also studied.

We measure the frequency of the low $m=0$ quadrupolar excitation mode of weakly interacting Bose-Einstein condensates in the transition region from the three-dimensional (3D) to the 1D mean-field regime. Various effects shifting the frequency of the mode are discussed. In particular we take the dynamic coupling of the condensate with the thermal component at finite temperature into account using a time-dependent Hartree-Fock-Bogoliubov treatment developed by Giorgini [Phys. Rev. A, 61, 063615 (2000)]. We show that the frequency rises in the transition from 3D to 1D, in good agreement with the theoretical prediction of Menotti and Stringari [Phys. Rev. A 66, 043610 (2002)].