Implementation of controlled rotations using entanglement is considered. We use a general two-qubit pure state to implement controlled rotations on two separate qubits. The probability of the success we achieve is higher than the known results in some parameter regions. Qualitatively the probability of the success we achieve is an increasing function of the entanglement and a decreasing function of the controlled-rotation angle, and the probability of success will approach a unit when the entangled state approaches a Bell state or the controlled-rotation angle approaches zero.

We study the transfer dynamics of nonclassical fluctuations of light to the ground-state collective spin components of an atomic ensemble during a pulsed quantum memory sequence, and evaluate the relevant physical quantities to be measured in order to characterize such a quantum memory. We show in particular that the fluctuations stored into the atoms are emitted in temporal modes which are always different from those of the readout pulse, but which can nevertheless be retrieved efficiently using a suitable temporal mode-matching technique. We give a simple toy model—a cavity with variable transmission—that accounts for the behavior of the atomic quantum memory.

By analyzing entangled photon states in terms of high-dimensional spatial mode superpositions, it becomes feasible to expose high-dimensional entanglement, and even the nonlocality of twin photons. To this end, a proper analyzer should be designed that is capable of handling a large number of spatial modes, while still being convenient to use in an experiment. We compare two variants of a high-dimensional spatial mode analyzer on the basis of classical and quantum considerations. These analyzers have been tested in classical optical experiments.

We show the propagation of entangled states of high-dimensional quantum systems. The qudits states were generated using the transverse correlation of the twin photons produced by spontaneous parametric down-conversion. Their free-space distribution was performed at the laboratory scale and the propagated states maintained a high fidelity with their original form. The use of entangled qudits allow an increase in the quantity of information that can be transmitted and may also guarantee more privacy for communicating parties. Therefore, studies about propagating entangled states of qudits are important for the effort of building quantum communication networks.

Hitting times for discrete quantum walks on graphs give an average time before the walk reaches an ending condition. To be analogous to the hitting time for a classical walk, the quantum hitting time must involve repeated measurements as well as unitary evolution. We derive an expression for hitting time using superoperators, and numerically evaluate it for the discrete walk on the hypercube. The values found are compared to other analogs of hitting time suggested in earlier work. The dependence of hitting times on the type of unitary “coin” is examined, and we give an example of an initial state and coin which gives an infinite hitting time for a quantum walk. Such infinite hitting times require destructive interference, and are not observed classically. Finally, we look at distortions of the hypercube, and observe that a loss of symmetry in the hypercube increases the hitting time. Symmetry seems to play an important role in both dramatic speed-ups and slow-downs of quantum walks.

Ultracold highly excited atoms in a magneto-optical trap (MOT) are strongly coupled by the dipole-dipole interaction. We have investigated the importance of many-body effects by controlling the dimensionality and density of the excited sample. We excited three different cylindrical volumes of atoms in the MOT to Rydberg states. At small radius, where the sample is nearly one-dimensional, many-body interactions are suppressed. At larger radii, the sample becomes three-dimensional and many-body effects are apparent.

We study the quantum limits in an optomechanical sensor based on a detuned high-finesse cavity with a movable mirror. We show that the radiation pressure exerted on the mirror by the light in the detuned cavity induces a modification of the mirror dynamics and makes the mirror motion sensitive to the signal. This leads to an amplification of the signal by the mirror dynamics, and to an improvement of the sensor sensitivity beyond the standard quantum limit, up to an ultimate quantum limit only related to the mechanical dissipation of the mirror. This improvement is somewhat similar to the one predicted in detuned signal-recycled gravitational-wave interferometers, and makes a high-finesse cavity a model system to test these quantum effects.

Stimulated Raman adiabatic passage (STIRAP) is a well-studied pump-probe control scheme for manipulating the population of quantum states of atoms or molecules. By encoding the digits to be operated on as “on” or “off” laser input signals we show how STIRAP can be used to implement a finite-state logic machine. The physical conditions required for an effective STIRAP operation are related to the physical conditions expected for a logic machine. In particular, a condition is derived on the mean number of photons that represent an on pulse. A finite-state machine computes Boolean expressions that depend both on the input and on the present state of the machine. With two input signals we show how to implement a full adder where the carry-in digit is stored in the state of the machine. Furthermore, we show that it is possible to store the carry-out digit as the next state and thereby return the machine to a state ready for the next full addition. Such a machine operates as a cyclical full adder. We further show how this full adder can equally well be operated as a full subtractor. To the best of our knowledge this is the first example of a nanosized system that implements a full subtraction.

We demonstrate control on nonadiabatic molecular alignment by using a spectrally phase-shaped laser pulse. An evolutionary algorithm in a closed feedback loop has been used in order to find pulse shapes that maximize a given effect. In particular, this scheme has been applied to the optimization of total alignment, and to the control of the temporal structure of the alignment transient within a revival. Asymmetric temporal pulse shapes have been found to be very effective for the latter and have been studied separately in a single-parameter control scheme. Our experimental results are supported by numerical simulations.

A tomographic technique is introduced in order to determine the quantum state of the center-of-mass motion of neutrons. Different reconstruction methods are compared and discussed. An experiment is proposed and numerically analyzed.

In standard coherent state teleportation with a shared two-mode squeezed vacuum (TMSV) state there is a trade-off between the teleportation fidelity and the fidelity of estimation of the teleported state from the results of the Bell measurement. Within the class of Gaussian operations this trade-off is optimal, i.e., there is not a Gaussian operation that would give a larger estimation fidelity for a given output fidelity. We show that this trade-off can be improved by up to 2.77% if we use a suitable non-Gaussian operation. This operation can be implemented by the standard teleportation protocol in which the shared TMSV state is replaced with a suitable non-Gaussian entangled state. We also demonstrate that this operation can be used to enhance the transmission fidelity of a certain noisy channel.

Quantum-state tomography—the practice of estimating a quantum state by performing measurements on it—is useful in a variety of contexts. We introduce “gentle tomography” as a version of tomography that preserves the measured quantum data. As an application of gentle tomography, we describe a polynomial-time method for universal source coding.

Using the experimental data on the energy-level shift of kaonic hydrogen in the ground state [Beer et al., Phys. Rev. Lett. 94, 212302 (2005)] and the theoretical value of the energy-level shift, calculated within the phenomenological quantum field theoretic approach to the description of strong low-energy $\overline{K}N$ and $\overline{K}NN$, interactions, we estimate the value of the ${\sigma }_{KN}^{(I=1)}\left(0\right)$ term of low-energy $\overline{K}N$ scattering. We get ${\sigma }_{KN}^{(I=1)}\left(0\right)=433\pm 132\mathrm{MeV}$. This shows the absence of strange quarks in the proton structure.

We present a diagrammatic approach for the dimer-dimer scattering problem in two or three spatial dimensions, within the resonance approximation where these dimers are in a weakly bound resonant state. This approach is first applied to the calculation of the dimer-dimer scattering length $a_B$ in three spatial dimensions, for dimers made of two fermions in a spin-singlet state, with corresponding scattering length $a_F$, and the already known result $a_B=0.60$ $a_F$ is recovered exactly. Then we make use of our approach to obtain results in two spatial dimensions for fermions as well as for bosons. Specifically, we calculate bound-state energies for three $bbb$ and four $bbbb$ resonantly interacting bosons in two dimensions. We consider also the case of a resonant interaction between fermions and bosons, and we obtain the exact bound-state energies of two bosons plus one fermion $bbf$, two bosons plus two fermions $b{f}_{\uparrow }b{f}_{\downarrow }$, and three bosons plus one fermion $bbbf$.

The response of quasi-one-dimensional very-high-$n$ Rydberg atoms to a periodic train of short unidirectional electric-field pulses, termed half-cycle pulses (HCPs), is studied at high scaled frequencies. Pronounced nonmonotonic structure in the survival probability is observed as $N$, the number of HCPs in the train is increased, the survival probability actually increasing with $N$ over certain ranges of $N$. This behavior is very sensitive to the polarization of the Rydberg states and is explained with the aid of classical simulations.

We study the sound velocity in cubic and noncubic three-dimensional optical lattices. We show how the van Hove singularity of the free Fermi gas is smoothed by interactions and eventually vanishes when interactions are strong enough. For noncubic lattices, we show that the speed of sound (Bogoliubov-Anderson phonon) shows clear signatures of dimensional crossover both in the one- and two-dimensional limits.

We study single-particle excitations of a Bose gas in an optical lattice in the Mott-insulator phase. The characteristic feature of the single-particle spectrum in the Mott-insulator phase is the existence of an energy gap between the particle and hole excitations. We show that the single-particle excitation energies and associated energy gap in the Mott-insulator phase can be directly probed by an output-coupling experiment. We apply the general expression for the output current derived by Luxat and Griffin, which is given in terms of the single-particle Green’s functions of a trapped Bose gas, to the Mott-insulator phase using the Bose-Hubbard model. The energy spectrum of the momentum-resolved output current exhibits two characteristic peaks corresponding to the particle and hole excitations, and thus it can be used to detect the transition point from the Mott insulator to superfluid phase where the energy gap disappears.

We propose two schemes for the generation of cluster states. One is based on cavity quantum electrodynamics (QED) techniques. The scheme only requires resonant interactions between two atoms and a single-mode cavity. The interaction time is very short, which is important in view of decoherence. Furthermore, we also discuss the cavity decay and atomic spontaneous emission case. The other is based on atomic ensembles. The scheme has an inherent fault tolerance function and is robust to realistic noise and imperfections. All the facilities used in our schemes are well within the current technology.

The electric-field-dependent $g$ factor of the ground state of ${}^2\Pi _{1∕2}$ molecules is predicted cross zero at a specific value of electric field. Furthermore, $Edg∕dE$ evaluated at this field is expected to be small, allowing for extremely precise zeroing of the molecular magnetic moment. For the PbF molecule, we estimate this field to be $68\mathrm{kV}∕\mathrm{cm}$. If this prediction is correct, PbF could provide a uniquely sensitive probe of the electric dipole moment of the electron.

We calculate the energy-momentum balance in quantum dielectrics such as Bose-Einstein condensates. In agreement with the experiment [G. K. Campbell et al., Phys. Rev. Lett. 94, 170403 (2005)] variations of the Minkowski momentum are imprinted onto the phase, whereas the Abraham tensor drives the flow of the dielectric. Our analysis indicates that the Abraham-Minkowski controversy has its root in the Röntgen interaction of the electromagnetic field in dielectric media.