Unconventional superfluid in a two-dimensional Fermi gas with anisotropic spin-orbit coupling and Zeeman fields

We study the phase diagram of a two-dimensional ultracold Fermi gas with the synthetic spin-orbit coupling (SOC) that has recently been realized at NIST. Due to the coexistence of anisotropic SOC and effective Zeeman fields in the NIST scheme, the system shows rich structure of phase separation involving exotic gapless superfluid and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing states with different center-of-mass momentum. In particular, we characterize the stability region of FFLO states and demonstrate their unique features under SOC. We then show that the effective transverse Zeeman field in the NIST scheme can qualitatively change the landscape of the thermodynamic potential which leads to intriguing effects such as the disappearance of pairing instability, the competition between different FFLO states, and the stabilization of a fully gapped FFLO state. These interesting features may be probed for example by measuring the in-situ density profiles or by the momentum-resolved radio-frequency spectroscopy.Comment: 7 pages, 6 figures. with updated figures and discussion

Variable-Rate Linear Network Error Correction MDS Codes

In network communication, the source often transmits messages at several different information rates within a session. How to deal with information transmission and network error correction simultaneously under different rates is introduced in this paper as a variable-rate network error correction problem. Apparently, linear network error correction MDS codes are expected to be used for these different rates. For this purpose, designing a linear network error correction MDS code based on the existing results for each information rate is an efficient solution. In order to solve the problem more efficiently, we present the concept of variable-rate linear network error correction MDS codes, that is, these linear network error correction MDS codes of different rates have the same local encoding kernel at each internal node. Further, we propose an approach to construct such a family of variable-rate network MDS codes and give an algorithm for efficient implementation. This approach saves the storage space for each internal node, and resources and time for the transmission on networks. Moreover, the performance of our proposed algorithm is analyzed, including the field size, the time complexity, the encoding complexity at the source node, and the decoding methods. Finally, a random method is introduced for constructing variable-rate network MDS codes and we obtain a lower bound on the success probability of this random method, which shows that this probability will approach to one as the base field size goes to infinity.Comment: Single column, 34 pages, submitted for publication. arXiv admin note: text overlap with arXiv:1311.7466, arXiv:1011.137

Construction of Network Error Correction Codes in Packet Networks

Recently, network error correction coding (NEC) has been studied extensively. Several bounds in classical coding theory have been extended to network error correction coding, especially the Singleton bound. In this paper, following the research line using the extended global encoding kernels proposed in \cite{zhang-correction}, the refined Singleton bound of NEC can be proved more explicitly. Moreover, we give a constructive proof of the attainability of this bound and indicate that the required field size for the existence of network maximum distance separable (MDS) codes can become smaller further. By this proof, an algorithm is proposed to construct general linear network error correction codes including the linear network error correction MDS codes. Finally, we study the error correction capability of random linear network error correction coding. Motivated partly by the performance analysis of random linear network coding \cite{Ho-etc-random}, we evaluate the different failure probabilities defined in this paper in order to analyze the performance of random linear network error correction coding. Several upper bounds on these probabilities are obtained and they show that these probabilities will approach to zero as the size of the base field goes to infinity. Using these upper bounds, we slightly improve on the probability mass function of the minimum distance of random linear network error correction codes in \cite{zhang-random}, as well as the upper bound on the field size required for the existence of linear network error correction codes with degradation at most $d$.Comment: 14 pages, submitted in 4 Nov. 201

Bose-Einstein condensate in an optical lattice with Raman-assisted two-dimensional spin-orbit coupling

In a recent experiment by Wu {\textit et al.} (arXiv:1511.08170), a Raman-assisted two-dimensional spin-orbit coupling has been realized for a Bose-Einstein condensate in an optical lattice potential. In light of this exciting progress, we study in detail key properties of the system. As the Raman lasers inevitably couple atoms to high-lying bands, the behaviors of the system in both the single- and many-particle sectors are significantly affected. In particular, the high-band effects enhance the plane-wave phase and lead to the emergence of "roton" gaps at low Zeeman fields. Furthermore, we identify high-band-induced topological phase boundaries in both the single-particle and the quasi-particle spectra. We then derive an effective two-band model, which captures the high-band physics in the experimentally relevant regime. Our results not only offer valuable insights into the novel two-dimensional lattice spin-orbit coupling, but also provide a systematic formalism to model high-band effects in lattice systems with Raman-assisted spin-orbit couplings.Comment: 10 pages, 5 figure

BCS-BEC crossover and quantum phase transition in an ultracold Fermi gas under spin-orbit coupling

In this work, we study the BCS-BEC crossover and quantum phase transition in a Fermi gas under Rashba spin-orbit coupling close to a Feshbach resonance. By adopting a two-channel model, we take into account of the closed channel molecules, and show that combined with spin-orbit coupling, a finite background scattering in the open channel can lead to two branches of solution for both the two-body and the many-body ground states. The branching of the two-body bound state solution originates from the avoided crossing between bound states in the open and the closed channels, respectively. For the many-body states, we identify a quantum phase transition in the upper branch regardless of the sign of the background scattering length, which is in clear contrast to the case without spin-orbit coupling. For systems with negative background scattering length in particular, we show that the bound state in the open channel, and hence the quantum phase transition in the upper branch, are induced by spin-orbit coupling. We then characterize the critical detuning of the quantum phase transition for both positive and negative background scattering lengths, and demonstrate the optimal parameters for the critical point to be probed experimentally.Comment: 7 pages, 4 figure

Three-component Fulde-Ferrell superfluids in a two-dimensional Fermi gas with spin-orbit coupling

We investigate the pairing physics of a three-component spin-orbit coupled Fermi gas in two spatial dimensions. The three atomic hyperfine states of the system are coupled by the recently realized synthetic spin-orbit coupling (SOC), which mixes different hyperfine states into helicity branches in a momentum-dependent manner. As a consequence, the interplay of spin-orbit coupling and the hyperfine-state dependent interactions leads to the emergence of Fulde-Ferrell (FF) pairing states with finite center-of-mass momenta even in the absence of the Fermi-surface asymmetry that is usually mandatory to stabilize an SOC-induced FF state. We show that, for different combinations of spin-dependent interactions, the ground state of the system can either be the conventional Bardeen-Cooper-Schrieffer pairing state with zero center-of-mass momentum or be the FF pairing states. Of particular interest here is the existence of a three-component FF pairing state in which every two out of the three components form FF pairing. We map out the phase diagram of the system and characterize the properties of the three-component FF state, such as the order parameters, the gapless contours and the momentum distributions. Based on these results, we discuss possible experimental detection schemes for the interesting pairing states in the system.Comment: 8 pages, 7 figures, updated references, published versio

Significance of dressed molecules in a quasi-two-dimensional polarized Fermi gas

We investigate the properties of a spin-orbit coupled quasi-two-dimensional Fermi gas with tunable s-wave interaction between the two spin species. By analyzing the two-body bound state, we find that the population of the excited states in the tightly-confined axial direction can be significant when the two-body binding energy becomes comparable or exceeds the axial confinement. Since the Rashba spin-orbit coupling that we study here tends to enhance the two-body binding energy, this effect can become prominent at unitarity or even on the BCS side of the Feshbach resonance. To study the impact of these excited modes along the third dimension, we adopt an effective two-dimensional Hamiltonian in the form of a two-channel model, where the dressed molecules in the closed channel consist of the conventional Feshbach molecules as well as the excited states occupation in the axial direction. With properly renormalized interactions between atoms and dressed molecules, we find that both the density distribution and the phase structure in the trap can be significantly modified near a wide Feshbach resonance. In particular, the stability region of the topological superfluid phase is increased. Our findings are helpful for the experimental search for the topological superfluid phase in ultra-cold Fermi gases, and have interesting implications for quasi-low-dimensional polarized Fermi gases in general.Comment: 10 pages, 7 figure

Realization of Probabilistic Identification and Clone of Quantum-States II Multiparticles System

We realize the probabilistic cloning and identifying linear independent quantum states of multi-particles system, given prior probability, with universal quantum logic gates using the method of unitary representation. Our result is universal for separate state and entanglement. We also provide the realization in the condition given $M$ initial copies for each state.Comment: 18 Pages, 3 Figures, ReVTe

Conditions for manipulation of a set of entangled pure states

We derive a sufficient condition for a set of pure states, each entangled in two remote $N$-dimensional systems, to be transformable to $k$-dimensional-subspace equivalent entangled states ($k\leq N$) by same local operations and classical communication. If $k=N$, the condition is also necessary. This condition reveals the function of the relative marginal density operators of the entangled states in the entanglement manipulation without sufficient information of the initial states.Comment: 5 Pages, no Figure, REVTeX. The generalization of quant-ph/990801

The superposition invariance of unitary operators and maximally entangled state

In this paper, we study the superposition invariance of unitary operators and maximally entangled state respectively. Furthermore, we discuss the set of orthogonal maximally entangled states. We find that orthogonal basis of maximally entangled states can be divided into k subspaces. It is shown that some entanglement properties of superposed state in every subspace are invariant