We report an interaction that controls spin squeezing in a collection of spin 1/2 particles. We describe how spin squeezing can be generated and maintained in time. Our scheme can be applied to control the spin squeezing in a Bose condensate with two internal spin states.Comment: 3 pages, 2 figure

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We study a two-level atom coupled to a Bose-Einstein condensate. We show that the rules governing the decoherence of mesoscopic superpositions involving different classical-like states of the condensate can be probed using this system. This scheme is applicable irrespective of whether the condensate is initially in a coherent, thermal or more generally in any mixture of coherent states. The effects of atom loss and finite temperature to the decoherence can therefore be studied. We also discuss the various noise sources causing the decoherence.

We study the decoherence of Majorana modes of a fermion chain, where the fermions interact with their nearest neighbours. We investigate the effect of dissipation and dephasing on the Majorana modes of a fermionic chain. The dissipative and dephasing noises induce the non-parity- and parity-preserving transitions between the eigenstates of the system, respectively. Therefore, these two types of noises lead to the different decoherence mechanisms. In each type of noise, we discuss the low- and high-frequency regimes to describe the different environments. We numerically calculate the dissipation and dephasing rates in the presence of long-range interactions. We find that the decoherence rate of interacting Majorana modes is different to that of non-interacting modes. We show the examples that the long-range interactions can reduce the decoherence rate. It is advantageous to the potential applications of quantum information processing.

We study the generation of two-mode entanglement in a two-component Bose-Einstein condensate trapped in a double-well potential. By applying the Holstein-Primakoff transformation, we show that the problem is exactly solvable as long as the number of excitations due to atom-atom interactions remains low. In particular, the condensate constitutes a symmetric Gaussian system, thereby enabling its entanglement of formation to be measured directly by the fluctuations in the quadratures of the two constituent components [Giedke {\it et al.}, Phys. Rev. Lett. {\bf 91}, 107901 (2003)]. We discover that significant two-mode squeezing occurs in the condensate if the interspecies interaction is sufficiently strong, which leads to strong entanglement between the two components.Comment: 22 pages, 4 figure

We study the dynamics of a pair of molecular ensembles trapped inside a superconducting resonator through which they are strongly coupled via a microwave field mode. We find that entanglement can be generated via "vacuum fluctuations" even when the molecules and cavity field are initially prepared in their ground state. This entanglement is created in a relatively short time and without the need for further manipulation of the system. It does, therefore, provide a convenient scheme to entangle two mesoscopic systems, and may well be useful quantum information processing. PACS numbers:Vacuum fluctuations can have important physical consequences, for example, in the Casimir effect [1] and Hawking radiation [2]. van der Waals interactions, i.e., attractive long-ranged interaction between neutral atoms or molecules, are also a kind of Casimir effect. It is an interesting question as to how vacuum fluctuations can be used to influence the properties of quantum entanglement between two systems. Quantum entanglement is a fundamental concept in quantum mechanics [3] and is also the physical resource in quantum information processing [4]. In fact, it has recently been shown possible to generate entanglement between a pair of particles via the vacuum modes of the radiation field [5,6,7].In this paper, we study how vacuum fluctuations induce quantum entanglement between two mesoscopic systems, i.e., polar molecular ensembles [8] are placed inside a cavity, and strongly coupled by a single microwave mode. Recently, Rabl et al. [9] have proposed the realization of a quantum memory using such ensembles of polar molecules inside a superconducting resonator [10]. The energy difference between two internal states of a polar molecule is the order of GHz and polar molecules have significant electric dipole moments. A strong coupling to a microwave field via a transmission line can thus be achieved. In addition to the strength of the coupling, low-lying collective excitations can be coupled to the field and exploit the enhanced coupling to them, which scales as √ N , where N is the number of molecules in the ensemble.The dynamics of vacuum fluctuations [11] is hard to observe in ordinary systems. To show why this is so, we start the simple case of a two-level atom interacting with a quantized field. Conventionally, we use the Jaynes-Cummings model [12] in the interaction picture,to describe a two-level system σ ± coupled to a quantized field b, for ω ′ 0 , ω ′ and g ′ are an energy difference between two-level atom, the frequency of the field and the Rabi frequency respectively. The rotating wave approximation (RWA) can usually be used because the two counteringrotating terms, bσ − and σ + b † , can be neglected; they carry a fast oscillation with the high frequency ω ′ + ω ′ 0 . The RWA is, therefore, an excellent approximation for the optical frequency regime in the weak Rabi coupling limit. Clearly, this Hamiltonian will produce no evolution in the atoms and the photon field if they both start in the irrespective ground states. H...

We study the precision limits of detecting a linear magnetic-field gradient by using W-states in the presence of different types of noises. We consider to use an atomic spin chain for probing the magnetic-field gradient, where a W-state is prepared. We compare this method with the measurement of using two uncorrelated atoms. For pure states, W-states can provide an improvement over uncorrelated states in determining the magnetic-field gradient up to four particles. We examine the effects of local dephasing and dissipations on the performances of detections. In presence of dephasing, the uncorrelated atoms can give a higher precision than using W-states. But W-states provide a better performance in the presence of dissipation for a few particles. We briefly discuss the implementation of the detection methods with cold atoms and trapped ions.Comment: 7 pages and 5 figures, title changed, updated version with clarificatio

We study the implementation of quantum phase measurement in a superconducting circuit, where two Josephson phase qubits are coupled to the photon field inside a resonator. We show that the relative phase of the superposition of two Fock states can be imprinted in one of the qubits. The qubit can thus be used to probe and store the quantum coherence of two distinguishable Fock states of the single-mode photon field inside the resonator. The effects of dissipation of the photon field on the phase detection are investigated. We find that the visibilities can be greatly enhanced if the Kerr nonlinearity is exploited. We also show that the phase measurement method can be used to perform the Gauss sum factorization of numbers (≥ 10 4 ) into a product of prime integers, as well as to precisely measure both the resonator's frequency and the nonlinear interaction strength. The largest factorizable number is mainly limited by the coherence time. If the relaxation time of the resonator were to be ∼ 10 µs (∼ 1 ms), then the largest factorizable number can be ≥ 10 4 N (≥ 10 7 N ), where N is the number of photons in the resonator.