We present a novel scheme for performing a conditional phase gate between two spin qubits in adjacent semiconductor quantum dots through delocalized single exciton states, formed through the interdot Förster interaction. We consider two resonant quantum dots, each containing a single excess conduction band electron whose spin embodies the qubit. We demonstrate that both the two-qubit gate and arbitrary single-qubit rotations may be realized to a high fidelity with current semiconductor and laser technology.

Within a systematic approach based on nonrelativistic quantum electrodynamics, we derive the one-loop self-energy correction of order $\alpha (Z\alpha {)}^4$ to the bound-electron $g$ factor. In combination with numerical data, this analytic result improves theoretical predictions for the self-energy correction for carbon and oxygen by an order of magnitude. Basing on one-loop calculations, we obtain the logarithmic two-loop contribution of order ${\alpha }^2(Z\alpha {)}^4\ln [(Z\alpha {)}^{-2}]$ and the dominant part of the corresponding constant term. The results obtained improve the accuracy of the theoretical predictions for the $1S$ bound-electron $g$ factor and influence the value of the electron mass determined from $g$-factor measurements.

We demonstrate the realization of a quantum register using a string of single neutral atoms which are trapped in an optical dipole trap. The atoms are selectively and coherently manipulated in a magnetic field gradient using microwave radiation. Our addressing scheme operates with a high spatial resolution, and qubit rotations on individual atoms are performed with 99% contrast. In a final readout operation we analyze each individual atomic state. Finally, we have measured the coherence time and identified the predominant dephasing mechanism for our register.

The Smoluchowski equation for irreversible aggregation in suspensions of equally charged particles is studied. Accumulation of charges during the aggregation process leads to a crossover from power-law to sublogarithmic cluster growth at a characteristic time and cluster size. For larger times the suspension is usually called stable, although aggregation still proceeds slowly. In this regime the size distribution evolves towards a universal scaling form, independent of any parameter included in the theory. The relative width falls off to a universal value ${\sigma }_{\mathrm{r}}^{\infty }\approx 0.2017$ that is much smaller than in the uncharged case. We conjecture that ${\sigma }_{\mathrm{r}}^{\infty }$ is a lower bound for the asymptotic relative width for all physical systems with irreversible aggregation.

The relation between thermodynamic phase transitions in classical systems and topology changes in their configuration space is discussed for a one-dimensional, analytically tractable solid-on-solid model. The topology of a certain family of submanifolds of configuration space is investigated, corroborating the hypothesis that, in general, a change of the topology within this family is a necessary condition in order to observe a phase transition. Considering two slightly differing versions of this solid-on-solid model, one showing a phase transition in the thermodynamic limit and the other not, we find that the difference in the quality or strength of this topology change appears to be insignificant. This example indicates the unattainability of a condition of exclusively topological nature which is sufficient to guarantee the occurrence of a phase transition in systems with nonconfining potentials.

We propose a scheme utilizing a quantum interference phenomenon to switch the transport of atoms in a 1D optical lattice through a site containing an impurity atom. The impurity represents a qubit which in one spin state is transparent to the probe atoms, but in the other acts as a single atom mirror. This allows a single-shot quantum nondemolition measurement of the qubit spin.

With a class of quantum heat engines which consists of two-energy-eigenstate systems undergoing, respectively, quantum adiabatic processes and energy exchanges with heat baths at different stages of a cycle, we are able to clarify some important aspects of the second law of thermodynamics. The quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realize Maxwell's demon. While respecting the second law on the average, they are also capable of extracting more work from the heat baths than is otherwise possible in thermal equilibrium.

We show that under the influence of pure vacuum noise two entangled qubits become completely disentangled in a finite-time, and in a specific example we find the time to be given by $\ln (\frac{2+\sqrt{2}}{2})$ times the usual spontaneous lifetime.

We describe a matter-wave amplifier for vibrational ground-state molecules which uses a Feshbach resonance to first form quasibound molecules starting from an atomic Bose-Einstein condensate. The quasibound molecules are then driven into their stable vibrational ground state via a two-photon Raman transition inside an optical cavity. The transition from the quasibound state to the electronically excited state is driven by a classical field. Amplification of ground state molecules is then achieved by using a strongly damped cavity mode for the transition from the electronically excited molecules to the molecular ground state.

We have experimentally studied the unstable dynamics of a harmonically trapped Bose-Einstein condensate loaded into a 1D moving optical lattice. The lifetime of the condensate in such a potential exhibits a dramatic dependence on the quasimomentum state. This is unambiguously attributed to the onset of dynamical instability, after a comparison with the predictions of the Gross-Pitaevskii theory. Deeply in the unstable region we observe the rapid appearance of complex structures in the atomic density profile, as a consequence of the condensate phase uniformity breakdown.

We present a theorem that all generalized Greenberger-Horne-Zeilinger states of a three-qubit system violate a Bell inequality in terms of probabilities. All pure entangled states of a three-qubit system are shown to violate a Bell inequality for probabilities; thus, one has Gisin’s theorem for three qubits.

We propose a method for quantum computation which uses control of spin-orbit coupling in a linear array of single electron quantum dots. Quantum gates are carried out by pulsing the exchange interaction between neighboring electron spins, including the anisotropic corrections due to spin-orbit coupling. Control over these corrections, even if limited, is sufficient for universal quantum computation over qubits encoded into pairs of electron spins. The number of voltage pulses required to carry out either single-qubit rotations or controlled-Not gates scales as the inverse of a dimensionless measure of the degree of control of spin-orbit coupling.

We consider gapped systems governed by either quantum or Markov dynamics, with the low-lying states below the gap being approximately degenerate. For a broad class of dynamics, we prove that ground or stationary state correlation functions can be written as a piece decaying exponentially in space plus a term set by matrix elements between the low-lying states. The key to the proof is a local approximation to the negative energy, or annihilation, part of an operator in a gapped system. Applications to numerical simulation of quantum systems and to networks are discussed.

A central challenge to the semiclassical description of quantum mechanics is the quantum phenomenon of “deep” tunneling. Here we show that real time classical trajectories suffice to account correctly even for deep quantum tunneling, using a recently formulated semiclassical initial value representation series of the quantum propagator and a prefactor free semiclassical propagator. Deep quantum tunneling is effected through what we term as coherent classical paths which are composed of one or more classical trajectories that lead from reactant to product but are discontinuous along the way. The end and initial phase space points of consecutive classical trajectories contributing to the coherent path are close to each other in the sense that the distance between them is weighted by a coherent state overlap matrix element. Results are presented for thermal and energy dependent tunneling through a symmetric Eckart barrier.

Bounds on the norm of quantum operators associated with classical Bell-type inequalities can be derived from their maximal eigenvalues. This quantitative method enables detailed predictions of the maximal violations of Bell-type inequalities.

A dark soliton oscillating in an elongated harmonically confined atomic Bose-Einstein condensate continuously exchanges energy with the sound field. Periodic optical paddles are employed to controllably enhance the sound density and transfer energy to the soliton, analogous to parametric driving. In the absence of damping, the amplitude of the soliton oscillations can be dramatically reduced, whereas with damping, a driven soliton equilibrates as a stable soliton with lower energy, thereby extending the soliton lifetime up to the lifetime of the condensate.

We propose a feasible optical setup allowing for a loophole-free Bell test with efficient homodyne detection. A non-Gaussian entangled state is generated from a two-mode squeezed vacuum by subtracting a single photon from each mode, using beam splitters and standard low-efficiency single-photon detectors. A Bell violation exceeding 1% is achievable with 6 dB squeezed light and a homodyne efficiency around 95%. A detailed feasibility analysis, based upon the recent experimental generation of single-mode non-Gaussian states, suggests that this method opens a promising avenue towards a complete experimental Bell test.

Because of their long coherence times, dopant ions have been considered promising candidates for scalable solid state quantum computing. Here we demonstrate a conditional phase shift between two qubits based on an optical transition of europium ions. The demonstration uses ensembles that have been selected from a randomly doped sample using spectral hole burning techniques. The electron dipole-dipole interaction between the ions that usually causes instantaneous spectral diffusion is used to generate the conditional phase shift.

There exists the famous circle theorem on the Yang-Lee zeros of the ferromagnetic Ising model. However, the Yang-Lee zeros of the antiferromagnetic Ising model are much less well understood than those of the ferromagnetic model. The precise distribution of the Yang-Lee zeros of the antiferromagnetic Ising model only with nearest-neighbor interaction $J$ on $L\times L$ square lattices is determined as a function of temperature $a=e^{2\beta J}$ ($J<0$), and its relation to the phase transitions is investigated. In the thermodynamic limit ($L\to \infty$), the distribution of the Yang-Lee zeros of the antiferromagnetic Ising model cuts the positive real axis in the complex $x=e^{-2\beta H}$ plane, resulting in the critical magnetic field $\pm H_c(a)$, where $H_c>0$ below the critical temperature $a_c=\sqrt{2}-1$. The results suggest that the value of the scaling exponent $y_h$ is 1 along the critical line for $a<a_c$.

We consider a two-species degenerate Fermi gas coupled by a diatomic Feshbach resonance. We show that the resulting superfluid can exhibit a form of coherent BEC-to-BCS oscillations in response to a nonadiabatic change in the system’s parameters, such as, for example, a sudden shift in the position of the Feshbach resonance. In the narrow resonance limit, the resulting solitonlike collisionless dynamics can be calculated analytically. In equilibrium, the thermodynamics can be accurately computed across the full range of BCS-BEC crossover, with corrections controlled by the ratio of the resonance width to the Fermi energy.