We generalize a proposal for detecting single-phonon transitions in a single nanoelectromechanical system (NEMS) to include the intrinsic anharmonicity of each mechanical oscillator. In this scheme two NEMS oscillators are coupled via a term quadratic in the amplitude of oscillation for each oscillator. One NEMS oscillator is driven and strongly damped and becomes a transducer for phonon number in the other measured oscillator. We derive the conditions for this measurement scheme to be quantum limited and find a condition on the size of the anharmonicity. We also derive the relation between the phase diffusion back-action noise due to number measurement and the localization time for the measured system to enter a phonon-number eigenstate. We relate both these time scales to the strength of the measured signal, which is an induced current proportional to the position of the read-out oscillator.

The effect of intersubsystem coupling on the Berry phase of a composite system as well as that of its subsystem is investigated. We analyze two coupled spin-$\frac{1}{2}$ systems with one driven by a quantized field as an example. The pure-state geometric phase of the composite system as well as the mixed-state geometric phase for the subsystem is calculated and discussed.

I construct a positive-operator-valued measure (POVM) which has $2d$ rank-1 elements and which is informationally complete for generic pure states in $d$ dimensions, thus confirming a conjecture made by Flammia, Silberfarb, and Caves (e-print quant-ph∕0404137). I show that if a rank-1 POVM is required to be informationally complete for all pure states in $d$ dimensions, it must have at least $3d-2$ elements. I also show that, in a POVM which is informationally complete for all pure states in $d$ dimensions, for any vector there must be at least $2d-1$ POVM elements which do not annihilate that vector.

The asymmetry parameter $\beta$ for the O $K$ shell photoemission of the CO molecule has been measured for different vibrational states of the residual ion. The corresponding calculations performed by us in the relaxed core Hartree-Fock approximation are in qualitative agreement with the experiment. From the analysis of theoretical data, we made the conclusion that the variation of $\beta$ with the vibrational quantum number is connected with different dependences of the dipole matrix elements in the $s\sigma$, $d\sigma$, and $f\sigma$ channels on the internuclear distance $R$ in the $\sigma *$ shape resonance.

We develop and apply an effective analytic theory of a noncollinear, broadband type-I parametric down-conversion to study a coupling efficiency of the generated photon pairs into single mode optical fibers. We derive conditions necessary for highly efficient coupling for single and double type-I crystal producing polarization entangled states of light. We compare the obtained approximate analytic expressions with the exact numerical solutions and discuss the results for a case of beta barium borate crystals.

We investigate an imbalance between the sensitivity of the common state measures—fidelity, trace distance, concurrence, tangle, von Neumann entropy, and linear entropy—when acted on by a depolarizing channel. Further, in this context we explore two classes of two-qubit entangled mixed states. Specifically, we illustrate a sensitivity imbalance between three of these measures for depolarized (i.e., Werner-state-like) nonmaximally entangled and maximally entangled mixed states, noting that the size of the imbalance depends on the state’s tangle and linear entropy.

We consider the cryptographic task of bit-string generation. This is a generalization of coin tossing in which two mistrustful parties wish to generate a string of random bits such that an honest party can be sure that the other cannot have biased the string too much. We consider a quantum protocol for this task, originally introduced in Phys. Rev. A 69, 022322 (2004), that is feasible with present day technology. We introduce security conditions based on the average bias of the bits and the Shannon entropy of the string. For each, we prove rigorous security bounds for this protocol in both noiseless and noisy conditions under the most general attacks allowed by quantum mechanics. Roughly speaking, in the absence of noise, a cheater can only bias significantly a vanishing fraction of the bits, whereas in the presence of noise, a cheater can bias a constant fraction, with this fraction depending quantitatively on the level of noise. We also discuss classical protocols for the same task, deriving upper bounds on how well a classical protocol can perform. This enables the determination of how much noise the quantum protocol can tolerate while still outperforming classical protocols. We raise several conjectures concerning both quantum and classical possibilities for large $n$ cryptography. An experiment corresponding to the scheme analyzed in this paper has been performed and is reported elsewhere.

We analyze the linear optical realization of number-sum Bell measurement and number-state manipulation by taking into account the realistic experimental situation, specifically imperfectness of single-photon detector. The present scheme for number-state manipulation is based on the number-sum Bell measurement, which is implemented with linear optical elements, i.e., beam splitters, phase shifters, and zero-one-photon detectors. Squeezed vacuum states and coherent states are used as optical sources. The linear optical Bell state detector is formulated quantum theoretically with a probability operator measure. Then, the fidelity of manipulation and preparation of number states, particularly for qubits and qutrits, is evaluated in terms of the quantum efficiency and dark count of single-photon detector. It is found that a high fidelity is achievable with small enough squeezing parameters and coherent state amplitudes.

We propose a scheme for the measurement of joint photon statistics and Wigner function of the entangled field states between two separate cavities. The scheme utilizes the momentum state of the two-level atoms in Bragg’s regime. The probability of finding the atom in any one of the momentum states is the product of joint photon statistics and an oscillatory function. The argument of the function contains the information of the joint photon numbers in two cavities. We use the method of state reduction to a single set of joint photon numbers, which is a consequence of the measuring sequence. The repeated measurement of the set of photon numbers gives the joint photon statistics of the entangled field state. The complete entangled state can be reconstructed as a Wigner function from the knowledge of photon statistics of the coherently displaced entangled state.

Here we consider perfect entanglers from another perspective. It is shown that there are some special perfect entanglers which can maximally entangle a full product basis. We explicitly construct a one-parameter family of such entanglers together with the proper product basis that they maximally entangle. This special family of perfect entanglers contains some well-known operators such as controlled-NOT (CNOT) and double-CNOT, but not $\sqrt{\mathrm{SWAP}}$. In addition, it is shown that all perfect entanglers with entangling power equal to the maximal value $\frac{2}{9}$ are also special perfect entanglers. It is proved that the one-parameter family is the only possible set of special perfect entanglers. Also we provide an analytic way to implement any arbitrary two-qubit gate, given a proper special perfect entangler supplemented with single-qubit gates. Such gates are shown to provide a minimum universal gate construction in that just two of them are necessary and sufficient in implementation of a generic two-qubit gate.

The static and dynamic properties of the alkaline-earth-metal atoms in their metastable state are computed in a configuration interaction approach with a semiempirical model potential for the core. Among the properties determined are the scalar and tensor polarizabilities, the quadrupole moment, some of the oscillator strengths, and the dispersion coefficients of the van der Waals interaction. A simple method for including the effect of the core on the dispersion parameters is described.

Electron energy and angular distributions are computed using the advanced adiabatic and the two-center Sturmian theory for the ionization of atomic hydrogen by proton impact at $5\mathrm{keV}$. The results are in accord with earlier observations that 50% of the electrons have energies less that $5\mathrm{eV}$. The electron energy and angular distributions are also computed using the top of the barrier propagator and previously reported benchmark solutions of the time-dependent Schrödinger equation on a lattice. The two very different theories agree well at $5\mathrm{keV}$ for electrons moving near the center of charge of the target and projectile nuclei.

We have measured the collisional self-broadening of the cesium $6S_{1∕2}\to 5D_{3∕2}$ electric quadrupole $\left(E2\right)$ transition at $689\mathrm{nm}$ for temperatures from $220\text{to}370°\mathrm{C}$, corresponding to cesium number densities from $3\times {10}^{15}\text{to}1.5\times {10}^{17}{\mathrm{cm}}^{-3}$. This $E2$ transition may have utility for studies of atomic parity nonconservation (PNC), and the collisional self-broadening represents an important systematic effect which must be understood for an accurate measurement of PNC. We find a value for this broadening of $1.32\pm 0.06\times {10}^{-8}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$, which is consistent with what would be expected for a quadrupole-quadrupole resonance interaction. To the best of our knowledge, no quantitative measurement of the self-broadening of an atomic $E2$ transition has been reported previously in the literature.

We describe a technique for creating superpositions of degenerate quantum states, such as are needed for beam splitters used in matter-wave optics, by manipulating the timing of three orthogonally polarized laser beams through which moving atoms (or molecules) pass; motion across the laser beams produces pulses in the atomic rest frame. As illustrated with representative simulations for transitions in metastable neon, a single pass through three overlapping laser beams can produce superpositions (with preselected phase) of atomic beams differing by transverse momentum corresponding to the momentum of four photons. Like the two-photon momentum transfer of the tripod linkage pattern which it extends, the method relies on controlled adiabatic time evolution in the Hilbert subspace of two degenerate dark states. It is thus a generalization to multiple dark states (and larger transfers of linear momentum to the atomic beam) of the single dark state occurring with the stimulated Raman adiabatic passage (STIRAP) technique, and therefore it is potentially insensitive to decoherence due to spontaneous emission. By extending the tripod-linkage system to more numerous degenerate states, the technique not only increases the atomic beam deflections but, as we demonstrate, allows control over the superposition phase and amplitudes. LIke other techniques based on adiabatic time evolution, the technique is robust with respect to variations of the intensity, timing, and other characteristics of the laser fields. Unlike STIRAP, the same robust partial population transfer occurs for opposite timings of the pulse sequence, as is needed for such procedures as Hadamard gates.

We examine the conditions needed to accomplish stimulated Raman adiabatic passage (STIRAP) when the three levels (ground $g$, excited $e$, and final $f$) are degenerate, with arbitrary couplings contributing to the pump-pulse interaction $\left(g\text{−}e\right)$ and to the Stokes-pulse interaction $\left(e\text{−}f\right)$. We show that in general a sufficient condition for complete population removal from the $g$ set of degenerate states for arbitrary, pure or mixed, initial state is that the degeneracies should not decrease along the sequence $g$, $e$, and $f$. Using a sequence of unitary transformations we demonstrate that when this condition holds it is possible to achieve the degenerate counterpart of conventional STIRAP, whereby adiabatic passage produces complete population transfer. Indeed, the system is equivalent to a set of independent three-state systems, in each of which a STIRAP procedure can be implemented. We also examine the cases when this degeneracy constraint does not hold and show what can be accomplished in those cases. For example, for angular momentum states when the degeneracy of the $g$ and $f$ levels is less than that of the $e$ level we show how a special choice for the pulse polarizations and phases can produce complete removal of population from the $g$ set. Our scheme can be a powerful tool for coherent control in degenerate systems, because of its robustness, when selective addressing of the states is not required or impossible. We illustrate the analysis with several analytically solvable examples, in which the degeneracies originate from angular momentum orientation, as expressed by magnetic sublevels.

We present a theoretical framework to describe the effects of decoherence on matter waves in Talbot-Lau interferometry. Using a Wigner description of the stationary beam the loss of interference contrast can be calculated in closed form. The formulation includes both the decohering coupling to the environment and the coherent interaction with the grating walls. It facilitates the quantitative distinction of genuine quantum interference from the expectations of classical mechanics. We provide realistic microscopic descriptions of the experimentally relevant interactions in terms of the bulk properties of the particles and show that the treatment is equivalent to solving the corresponding master equation in paraxial approximation.

We study the Mott-insulator transition of bosonic atoms in optical lattices. Using perturbation theory, we analyze the deviations from the mean-field Gutzwiller ansatz, which become appreciable for intermediate values of the ratio between hopping amplitude and interaction energy. We discuss corrections to number fluctuations, order parameter, and compressibility. In particular, we improve the description of the short-range correlations in the one-particle density matrix. These corrections are important for experimentally observed expansion patterns, both for bulk lattices and in a confining trap potential.

We study how coherent Stokes and anti-Stokes Raman scattering influence coherent population trapping. In an experiment using an atomic sodium vapor cell we observe induced transparency, induced absorption, and gain features, all of subnatural linewidth. The electromagnetically induced resonance is a peak or a dip depending on which side of the optical transition the fields are tuned to, and thus whether coherent anti-Stokes Raman scattering or coherent Stokes Raman scattering is the dominant process.

Following a recent theoretical proposal [J. Fiurášek and N. J. Cerf, Phys. Rev. Lett. 93, 063601 (2004)], we experimentally implement a scheme to measure the squeezing and purity of a single-mode squeezed vacuum state without an interferometric homodyne detection. The suggested setup is based on only a tunable beam splitter and a direct single-photon detector to fully characterize the generated Gaussian states. We discuss the experimental implementation of this procedure and compare it to other reference methods. A detailed exploitation of our results highlights some practical limitations of this method. This experimental work is followed by a detailed numerical analysis to derive the conditions required for the procedure to succeed. In particular, it is found that an overall single-photon detection efficiency of about 50% is needed, which is difficult to achieve in the present experiment.

We propose the cavity quantum electrodynamics method, using dispersive interaction between atoms and a high-quality cavity to realize the mesoscopic superposition of coherent states that would exhibit sub-Planck structures in phase space, i.e., the structures at a scale smaller than the Plank’s constant $\left(\hslash \right)$. These structures are direct signatures of quantum coherence and are formed as a result of interference between the two superposed cat states. In particular we focus on a superposition involving four coherent states. We show interferences in the conditional measurements involving two atoms.