[en] We have identified a class of many-body problems with analytic solution beyond the mean-field approximation. This is the case where each body can be considered as an element of an assembly of interacting particles that are translationally frozen multi-level quantum systems and that do not change significantly their initial quantum states during the evolution. In contrast, the entangled collective state of the assembly experiences an appreciable change. We apply this approach to interacting three-level systems

[en] We consider the effect of long-range dipole-dipole interaction on the excitation exchange dynamics of cold two-level atomic gases in the conditions where the size of the atomic cloud is large as compared to the wavelength of the dipole transition. We show that this interaction results in population redistribution across the atomic cloud and in specific spectra of the spontaneous photons emitted at different angles with respect to the direction of atomic polarization.

[en] In this paper, we review an open-loop evolution control method, called nonholonomic control, based on the alternate application of only two physical perturbations for timings which play the role of adjustable control parameters. We present the algorithm which allows one to explicitly compute the pulse sequence achieving any arbitrarily prescribed unitary evolution in a nonholonomic system, i.e. a system subject to two physical perturbations which, together with the natural Hamiltonian of the system, span the entire Lie algebra u(N). We moreover expose two extensions of our method to open quantum systems which, respectively, aim at preserving the information stored in the system and safely processing this information. The first is based on a generalization of the quantum Zeno effect, while the second is inspired by decoupling pulse techniques. The most important feature of the methods presented here is their universality: they indeed do not rely on any specific assumption on the system, which in particular is not bound to be a collection of two-level systems, or the error model considered, as is usually the case in the literature. Numerical and physical applications of our techniques are also provided.

[en] We design a scheme for detecting a single photon loss from multi-modal quantum signals transmitted via a fiber or in free space. This consists of a special type of unitary coding transformation, the parity controlled-squeezing, applied prior to the transmission on the signal composed by information and ancilla modes. At the receiver, the inverse unitary transformation is applied—decoding, and the ancilla mode is measured via photon detection. The outcome reveals whether a photon loss has occurred. Distortion of the information part of the signal caused by an ancilla photon loss can be corrected via unitary transformation while loss of a photon from the information part of the signal can be detected with the probability exponentially close to unity but cannot be corrected. In contrast to the schemes of decoherence free subspaces and quantum error correction protocols, this method allows one to make use in principle of entire Hilbert space dimensionality. We discuss possible ways of synthesizing the required encoding–decoding transformation. (paper)

[en] Conventionally, the effect of measurements on a quantum system is assumed to introduce decoherence, which renders the system classical-like. We consider here a microscopic meter, that is, an auxiliary essentially quantum system whose state is measured repeatedly, and show that it can be employed to induce transitions from classical states into inherently quantumlike states. The meter state is assumed to be lost in the environment and we derive a non-Markovian master equation for the dynamic system in the case of nondemolition coupling to the meter; this equation can be cast in the form of an (N_a)th-order differential equation in time, where N_a is the dimension of the meter basis. We apply the approach to a harmonic oscillator coupled to a spin-(1/2) meter and demonstrate how it can be used to engineer effective Hamiltonian evolution, subject to decoherence induced by the projective meter measurements

[en] The possibility of performing the C-NOT gate operation at the ground and the first excited states of two harmonic oscillators interacting via a two-level system subject to complete control is demonstrated. The system resembles Turing machine, where the result of interaction between oscillators and the two-level system is restricted to a certain fixed unitary transformation matrix, while all the control required for the implementation of the gate is provided via manipulations with the two-level system, which remains the only fully-controllable part of the entire system. Each gate operation requires a ‘Turing programming’, which can be realized as a series of $\gtrsim <!--\; ???\; -->63$ elementary unitary operations. The result shows a way how one can construct a quantum processor in a multimode microwave cavity equipped with a fully controlled two-level system, such as a Josephson-junction chip. Parameters of already existing experimental devises could allow one to perform up to 15 gate operations in an ensemble of about 10 qubits. (letter)

[en] We show that the multidimensional Zeno effect combined with non-holonomic control allows one to efficiently protect quantum systems from decoherence by a method similar to classical random coding. The method is applicable to arbitrary error-inducing Hamiltonians and general quantum systems. The quantum encoding approaches the Hamming upper bound for large dimension increases. Applicability of the method is demonstrated with a seven-qubit toy computer

[en] The protection of the coherence of open quantum systems against the influence of their environment is a very topical issue. A scheme is proposed here which protects a general quantum system from the action of a set of arbitrary uncontrolled unitary evolutions. This method draws its inspiration from ideas of standard error correction (ancilla adding, coding and decoding) and the quantum Zeno effect. A demonstration of our method on a simple atomic system--namely, a rubidium isotope--is proposed