Renormalization Group Analysis of a Confined, Interacting Bose Gas

The renormalization group is not only a powerful method for describing universal properties of phase transitions but it is also useful for evaluating non- universal properties beyond mean-field theory. In this contribution we concentrate on these latter aspects of the renormalization group approach. We introduce its main underlying ideas in the familiar context of the ideal Bose gas and then apply them to the case of an interacting, confined Bose gas within the framework of the random phase approximation. We model confinement by periodic boundary conditions and demonstrate how confinement modifies the flow equations of the renormalization group changing thus the thermodynamic properties of the gas.Comment: 24 pages, 5 figure

Cooperative quantum electrodynamical processes in an ellipsoidal cavity

We investigate spontaneous photon emission and absorption processes of two two-level atoms trapped close to the focal points of an ellipsoidal cavity, thereby taking into account the full multimode scenario. In particular, we calculate the excitation probabilities of the atoms by describing the field modes semiclassically. Based on this approach, we express the excitation probabilities by a semiclassical photon path representation. Due to the special property of an ellipsoidal cavity of having two focal points, we are able to study interesting intermediate instances between well-known quantum-optical scenarios. Furthermore, the semiclassical photon path representation enables us to address the corresponding retardation effects and causality questions in a straightforward manner.Comment: 14 pages, 3 figures, Optics and its Application

Constructing Pauli pulse schemes for decoupling and quantum simulation

Dynamical decoupling is a powerful technique to suppress errors in quantum systems originating from environmental couplings or from unwanted inter-particle interactions. However, it can also be used to selectively decouple specific couplings in a quantum system. We present a simple and easy-to-use general method to construct such selective decoupling schemes on qubit and qudit networks by means of (generalized) Pauli operations. As these constructed schemes can suppress Hamiltonian interactions on general qudit networks selectively, they are well suited for purposes of approximate quantum simulation. Some examples are presented, demonstrating the use of our method and the resulting decoupling schemes.Comment: 11 pages, 5 figure

Pulse-controlled quantum gate sequences on a strongly coupled qubit chain

We propose a selective dynamical decoupling scheme on a chain of permanently coupled qubits with XX type interactions, which is capable of dynamically suppressing any coupling in the chain by applying sequences of local pulses to the individual qubits. We demonstrate that high-fidelity single- and two-qubit gates can be achieved by this procedure and that sequences of gates can be implemented by this pulse control alone. We discuss the applicability and physical limitations of our model specifically for strongly coupled superconducting flux qubits. Since dynamically modifying the couplings between flux qubits is challenging, they are a natural candidate for our approach.Comment: 10 pages, 7 figure

Perfect excitation of a matter qubit by a single photon in free space

We propose a scheme for perfect excitation of a single two-level atom by a single photon in free space. The photon state has to match the time reversed photon state originating from spontaneous decay of a two-level system. We discuss its experimental preparation. The state is characterized by a particular asymmetric exponentially-shaped temporal profile. Any deviations from this ideal state limit the maximum absorption. Although perfect excitation requires an infinite amount of time we demonstrate that there is a class of initial one-photon quantum states which can achieve almost perfect absorption even for a finite interaction time. Our results pave the way for realizing perfect coupling between flying and stationary qubits in free space thus opening a possibility for building scalable quantum networks.Comment: 4 pages, 2 figure

Efficient single photon absorption by a trapped moving atom

The influence of the center of mass motion of a trapped two level system on efficient resonant single photon absorption is investigated. It is shown that this absorption process depends strongly on the ratio between the characteristic time scales of spontaneous photon emission and of the two level system's center of mass motion. In particular, if the spontaneous photon emission process occurs almost instantaneously on the time scale of the center of mass motion coherent control of the center of mass motion offers interesting perspectives for optimizing single photon absorption. It is demonstrated that this way time dependent modulation of a harmonic trapping frequency allows to squeeze the two level system's center of mass motion so strongly that high efficient single photon absorption is possible even in cases of weak confinement by a trapping potential.Comment: 9 pages, 5 figure

Selective dynamical decoupling for quantum state transfer

State transfer across discrete quantum networks is one of the elementary tasks of quantum information processing. Its aim is the faithful placement of information into a specific position in the network. However, all physical systems suffer from imperfections, which can severely limit the transfer fidelity. We present selective dynamical decoupling schemes which are capable of stabilizing imperfect quantum state transfer protocols on the model of a bent linear qubit chain. The efficiency of the schemes is tested and verified in numerical simulations on a number of realistic cases. The simulations demonstrate that these selective dynamical decoupling schemes are capable of suppressing unwanted errors in quantum state transfer protocols efficiently.Comment: 20 pages, 9 figure

Conditions for the existence of positive operator valued measures

Sufficient and necessary conditions are presented for the existence of $(N,M)$-positive operator valued measures ($(N,M)$-POVMs) valid for arbitrary-dimensional quantum systems. A sufficient condition for the existence of $(N,M)$-POVMs is presented. It yields a simple relation determining an upper bound on the continuous parameter of an arbitrary $(N,M)$-POVM, below which all its POVM elements are guaranteed to be positive semidefinite. Necessary conditions are derived for the existence of optimal $(N,M)$-POVMs. One of these necessary conditions exhibits a close connection between the existence of optimal informationally complete $(N,M)$-POVMs and the existence of isospectral, traceless, orthonormal, hermitian operator bases in cases, in which the parameter $M$ exceeds the dimension of the quantum system under consideration. Another necessary condition is derived for optimal $(N,M)$-POVMs, whose parameter $M$ is less than the dimension of the quantum system. It is shown that in these latter cases all POVM elements necessarily are projection operators of equal rank. This significantly constrains the possible parameters for constructing optimal $(N,M)$-POVMs. For the special case of $M=2$ a necessary and sufficient condition for the existence of optimal $(N,2)$-POVMs is presented

Typical bipartite steerability and generalized local quantum measurements

Recently proposed correlation-matrix based sufficient conditions for bipartite steerability from Alice to Bob are applied to local informationally complete positive operator valued measures (POVMs) of the $(N,M)$-type. These POVMs allow for a unified description of a large class of local generalized measurements of current interest. It is shown that this sufficient condition exhibits a peculiar scaling property. It implies that all types of informationally complete $(N,M)$-POVMs are equally powerful in detecting bipartite steerability from Alice to Bob and, in addition, they are as powerful as local orthonormal hermitian operator bases (LOOs). In order to explore the typicality of steering numerical calculations of lower bounds on Euclidean volume ratios between steerable bipartite quantum states from Alice to Bob and all quantum states are determined with the help of a hit-and-run Monte-Carlo algorithm. These results demonstrate that with the single exception of two qubits this correlation-matrix based sufficient condition significantly underestimates these volume ratios. These results are also compared with a recently proposed method which reduces the determination of bipartite steerability from Alice's qubit to Bob's arbitrary dimensional quantum system to the determination of bipartite entanglement. It is demonstrated that in general this method is significantly more effective in detecting typical steerability provided entanglement detection methods are used which transcend local measurements