Measurements in quantum mechanics cannot perfectly distinguish all states and necessarily disturb the measured system. We present and analyze a proposal to demonstrate fundamental limits on quantum control of a single qubit arising from these properties of quantum measurements. We consider a qubit prepared in one of two nonorthogonal states and subsequently subjected to dephasing noise. The task is to use measurement and feedback control to attempt to correct the state of the qubit. We demonstrate that projective measurements are not optimal for this task, and that there exists a nonprojective measurement with an optimum measurement strength which achieves the best trade-off between gaining information about the system and disturbing it through measurement backaction. We study the performance of a quantum control scheme that makes use of this weak measurement followed by feedback control, and demonstrate that it realizes the optimal recovery from noise for this system. We contrast this approach with various classically inspired control schemes.

It has recently been shown that finding the optimal measurement on the environment for stationary linear quadratic Gaussian control problems is a semidefinite program. We apply this technique to the control of the Einstein-Podolsky-Rosen correlations between two bosonic modes interacting via a parametric Hamiltonian at steady state. The optimal measurement turns out to be nonlocal homodyne measurement—the outputs of the two modes must be combined before measurement. We also find the optimal local measurement and control technique. This gives the same degree of entanglement but a higher degree of purity than the local technique previously considered [S. Mancini, Phys. Rev. A 73, 010304(R) (2006)].

We deal with many-electron systems having a noninteger number of electrons, which cannot be described properly by means of pure states or by canonical statistical ensemble states. The study of the one-electron reduced density matrix for these systems raises the problem of its representability in statistical ensembles of grand canonical type. We derive the necessary and sufficient conditions for the representability of the one-electron reduced density matrix of grand-canonical statistical ensembles.

We investigate both theoretically and experimentally the momentum distribution of multiply charged ions ionized by an intense multicycle laser field with a maximum intensity of $\sim (50–70)\mathrm{PW}∕{\mathrm{cm}}^2$. Ions with different charge states are produced during a single laser shot due to a spatial variation of the laser intensity within the beam focus. The measurements show approximately a simple linear relation between the width of the momentum distributions and the ionization potential of the ions. Such a power law scaling appears to be universal for various rare gas atoms used (He, Ne, Ar). We analyze this ionization dynamics using a quasiclassical tunneling theory for a single active electron model assuming that the interaction between electrons is negligible in such a strong field limit. We show that for the relatively long pulses used in the present work ($\sim 200\mathrm{fs}$ or $\sim 80\text{cycles}$) the effect of the laser envelope plays an important role in the ionization process.

We investigate the ground-state properties of an equal mixture of two species of bosons in its Mott-insulator phase at a filling factor of two per site. We identify one type of spin triplet-singlet transition through the competition of the ground state. When the on-site interaction is weak $(U<U_c)$ the two particles prefer to stay in the lowest band and with weak tunneling between neighboring sites the system is mapped into an effective spin-1 ferromagnetic exchange Hamiltonian. When the interaction is tuned by a Feshbach resonance to be large enough $(U>U_c)$, the higher band will be populated. Due to the orbital coupling term $S^{+}{S}^{-}$ in the Hamiltonian, the two atoms in different orbits on a site would form an on-site singlet. For a non-SU(2)-symmetric model, easy-axis or easy-plane ferromagnetic spin exchange models may be realized, corresponding to phase separation or counterflow superfluidity, respectively.

We propose a scheme to implement an $N$-qubit conditional phase gate with $N$ neutral atoms which are trapped in a large detuning optical cavity. In our scheme, since the cavity field is only required to be virtually excited, the phase gate operation is insensitive to the cavity decay and the gate can be implemented with a high fidelity.

A formal analytic solution of the time-dependent Schrödinger equation is obtained for cutoff Gaussian wavepackets incident on finite range potentials of arbitrary shape. We derive closed analytical expressions for transmitted wavepackets with a small cutoff and the solutions are applied to investigate the dynamics of wavepacket tunneling. We showed that the analytic solutions satisfy a useful rescaling property that was applied to study and characterize the delay time in delta potential barriers.

The intrinsic relationship between the maximum-likelihood quantum-state estimation and the representation of the signal is elaborated. A quantum analogy of the transfer function determines the space where a successful reconstruction can be achieved. This provides a tool for reducing the number of dimensions of the observed system based on physical characteristics of the reconstruction scheme rather than some ad hoc truncations. The method is illustrated with two examples of practical importance: an optical quantum homodyne tomography and a simple and robust tomography of an optical signal recorded by realistic binary detectors.

A system consisting of two single-mode cavities spatially separated and connected by an optical fiber and multiple two-level atoms trapped in the cavities is considered. If the atoms resonantly and collectively interact with the local cavity fields but there is no direct interaction between the atoms, we show that an ideal quantum state transfer and highly reliable quantum swap, entangling, and controlled-Z gates can be deterministically realized between the distant cavities. We find that the operation of state transfer and swap, entangling, and controlled-Z gates can be greatly speeded up as number of the atoms in the cavities increases. We also notice that the effects of spontaneous emission of atoms and photon leakage out of cavity on the quantum processes can also be greatly diminished in the multiatom case.

We study the effect of a phase shift on the amount of transferable two-spin entanglement in a spin chain. We consider a ferromagnetic Heisenberg or $XY$ spin chain, both numerically and analytically, and two mechanisms to generate a phase shift, the Aharonov-Casher effect, and the Dzyaloshinskii-Moriya interaction. In both cases, the maximum attainable entanglement is shown to be significantly enhanced, suggesting its potential usefulness in quantum information processing.

Inelastic collisions of ultracold atoms or molecules are analyzed using very general arguments. In free space, the deactivation rate can be enhanced or suppressed together with the scattering length of the corresponding elastic collision via a Feshbach resonance, and by interference of deactivation of the closed and open channels. In reduced dimensional geometries, the deactivation rate decreases with decreasing collision energy and does not increase with resonant elastic scattering length. This has broad implications; e.g., stabilization of molecules in a strongly confining two-dimensional optical lattice, since collisional decay of excited states due to inelastic collisions is suppressed. The relation of our results to the Lieb-Liniger model for bosonic atoms is addressed.

Recent advances have realized the direct variational calculation of the two-particle reduced density matrix (RDM) for electronic systems [Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)], but such an approach has yet to be explored for studying the ground-state motion of nuclei. In this paper we develop a few-particle variational RDM theory for treating ground-state nuclear motion in atomic and molecular clusters and potentially molecules. Two features of the RDM method for nuclear motion that differ from the electronic theory are the derivation and application of generalized $N$-representability conditions for (i) multiple types of particles and (ii) three- or higher-body interactions. Illustrative applications are made to helium nuclei in one and two dimensions and a simple organic molecule where the effects of particle statistics and classical and quantum limits are examined. Calculations are performed in computationally expensive and yet flexible numerical grid basis sets. As interparticle interactions are increased, the emergence of molecular structure from a Bose condensate is observed. Limitations and possibilities for the treatment of general molecular systems are discussed.

We have studied the efficiency of spin-exchange optical pumping (SEOP) in cells that contain either pure rubidium, mixtures of rubidium and potassium, or pure potassium. Optical pumping was performed with spectrally narrowed diode array lasers operating at either the wavelength of the Rb $5s_{1∕2}-5p_{1∕2}$ transition $\left(795\mathrm{nm}\right)$ or the K $4s_{1∕2}-4p_{1∕2}$ transition $\left(770\mathrm{nm}\right)$. Calculations of the expected efficiency are shown for practical conditions and compared to measurements. We have measured the vapor density ratio in Rb-K mixture cells using absorption of white light. Our focus is on the conditions that are relevant for neutron spin filters, but the results are relevant to all applications of SEOP. We find that both Rb-K and pure K cells yield improvements in the spin-exchange efficiency, and each approach has its own advantages. Overall, the best results for high polarizing rate with high polarization were obtained with mixture cells with K-Rb vapor density ratios between 2 and 6.

The exact analytical solution of the degenerate Landau-Zener model, wherein two bands of degenerate energies cross in time, is presented. The solution is derived by using the Morris-Shore transformation, which reduces the fully coupled system to a set of independent nondegenerate two-state systems and a set of decoupled states. Due to the divergence of the phase of the off-diagonal element of the propagator in the original Landau-Zener model, not all transition probabilities exist for infinite time duration. In general, apart from some special cases, only the transition probabilities between states within the same degenerate set exist, but not between states of different sets. An illustration is presented for the transition between the magnetic sublevels of two atomic levels with total angular momenta $J=2$ and 1.

We study the dynamics of the quantum phase transition of a ferromagnetic spin-1 Bose-Einstein condensate (BEC) from the polar phase to the broken-axisymmetry phase by changing magnetic field, and find the spontaneous formation of spinor domain walls followed by the creation of polar-core spin vortices. We also find that the spin textures depend very sensitively on the initial noise distribution, and that an anisotropic and colored initial noise is needed to reproduce the Berkeley experiment [Sadler et al., Nature (London) 443, 312 (2006)]. The dynamics of vortex nucleation and the number of created vortices depend also on the manner in which the magnetic field is changed. We point out an analogy between the formation of spin vortices from domain walls in a spinor BEC and that of vortex-antivortex pairs from dark solitons in a scalar BEC.

Measurements of the energy loss of protons and deuterons channeled in a very thin single-crystal foil of gold were performed, covering the range of very low velocities. The experimental results provide clear evidence of the deviation of the energy loss from the proportionality with ion velocity predicted theoretically, showing a transition between two well-defined regimes. We explain this behavior by a theoretical analysis that takes into account the electronic band structure properties of the medium, separating the contribution of the conduction band (described as a free Fermi gas) from the contribution of the nearly free $d$ electrons of gold, which are affected by a threshold behavior due to the shift of the density of states of this band with respect to the Fermi level. The theoretical model yields a very good description of the experimental findings.

We analyze a quantum optical memory based on the off-resonant Raman interaction of a single broadband photon, copropagating with a classical control pulse, with an atomic ensemble. The conditions under which the memory can perform optimally are found, by means of a universal mode decomposition. This enables the memory efficiency to be specified in terms of a single parameter, and the control field pulse shape to be determined via a simple nonlinear scaling. We apply the same decomposition to determine the optimal configurations for read-out.

We develop a circuit theory that enables us to analyze quantum measurements on a two-level system and on a continuous-variable system on an equal footing. As a measurement scheme applicable to both systems, we discuss a swapping state measurement that exchanges quantum states between the system and the measuring apparatus before the apparatus meter is read out. This swapping state measurement has an advantage in gravitational-wave detection over contractive state measurement in that the postmeasurement state of the system can be set to a prescribed one, regardless of the outcome of the measurement.

What is the time-optimal way of realizing quantum operations? Here, we show how important instances of this problem can be related to the study of shortest paths on the surface of a sphere under a special metric. Specifically, we provide an efficient synthesis of a controlled-NOT (CNOT) gate between qubits (spins $\frac{1}{2}$) coupled indirectly via Ising-type couplings to a third spin. Our implementation of the CNOT gate is significantly shorter than conventional approaches. The pulse sequences for efficient manipulation of our coupled spin system are obtained by explicit computation of geodesics on a sphere under the special metric. These methods are also used for the efficient synthesis of indirect couplings and of the Toffoli gate. We provide experimental realizations of the presented methods on a linear three-spin chain with Ising couplings.

We introduce a technique that allows one to connect any two arbitrary (pure or mixed) superposition states of an $N$-state quantum system. The proposed solution to this inverse quantum mechanical problem is analytical, exact, and very compact. The technique uses standard and generalized quantum Householder reflections (QHRs), which require external pulses of precise areas and frequencies. We show that any two pure states can be linked by just a single generalized QHR. The transfer between any two mixed states with the same dynamic invariants (e.g., the same density matrix eigenvalues) requires in general $N$ QHRs. Moreover, we propose recipes for synthesis of arbitrary preselected mixed states using a combination of QHRs and incoherent processes (pure dephasing or spontaneous emission).