Geometric phase of the one-dimensional Ising chain in a longitudinal field

For the one-dimensional Ising chain with spin-$1/2$ and exchange couple $J$ in a steady transverse field(TF), an analytical theory has well been developed in terms of some topological order parameters such as Berry phase(BP). For a TF Ising chain, the nonzero BP which depends on the exchange couple and the field strength characterizes the corresponding symmetry breaking of parity and time reversal(PT). However, there seems to exist a topological phase transition for the one-dimensional Ising chain in a longitudinal field(LF) with the reduced field strength $\epsilon$. If the LF is added at zero temperature, researchers believe that the LF also could influence the PT-symmetry and there exists the discontinuous BP. But the theoretic characterization has not been well founded. This paper tries to aim at this problem. With the Jordan-Wigner transformation, we give the four-fermion interaction form of the Hamiltonian in the one-dimensional Ising chain with a LF. Further by the method of Wick's theorem and the mean-field theory, the four-fermion interaction is well dealt with. We solve the ground state energy and the ground wave function in the momentum space. We discuss the BP and suggest that there exist nonzero BPs when $\epsilon=0$ in the paramagnetic case where $J<0$ and when $-1<\epsilon<1$, in the diamagnetic case where $J>0$.Comment: 14 pages, 2 table

Criterion for distinguishability of arbitrary bipartite orthogonal states

In this paper we present a necessary and sufficient condition of distinguishability of bipartite quantum states. It is shown that the operators to reliably distinguish states need only rounds of projective measurements and classical comunication. We also present a necessary condition of distinguishability of bipartite quantum states which is simple and general. With this condition one can get many cases of indistinguishability. The conclusions may be useful in understanding the essence of nonlocality and calculating the distillable entanglement and the bound of distillable entanglement.Comment: 7 page

Distinguishing locally of quantum states and the distillation of entanglement

This paper try to probe the relation of distinguishing locally and distillation of entanglement. The distinguishing information (DI) and the maximal distinguishing information (MDI) of a set of pure states are defined. The interpretation of distillation of entanglement in term of information is given. The relation between the maximal distinguishing information and distillable entanglement is gained. As a application of this relation the distillable entanglement of Bell-diagonal states is present.Comment: 5 page

Local distinguishability of quantum states and the distillation of entanglement

This paper tries to probe the relation between the local distinguishability of orthogonal quantum states and the distillation of entanglement. An new interpretation for the distillation of entanglement and the distinguishability of orthogonal quantum states in terms of information is given, respectively. By constraining our discussion on a special protocol we give a necessary and sufficient condition for the local distinguishability of the orthogonal pure states, and gain the maximal yield of the distillable entanglement. It is shown that the information entropy, the locally distinguishability of quantum states and the distillation of entanglement are closely related.Comment: 4 page, the revision of quant-ph/0202165, submitte

Distilling multipartite pure states from a finite number of copies of multipartite mixed states

This paper will address the question of the distillation of entanglement from a finite number of multi-partite mixed states. It is shown that if one can distill a pure entangled state from n copies of a mixed state $\sigma _{ABC...}$ there must be at least a subspace in whole Hilbert space of the all copies such that the projection of $\sigma_{ABC...}^{\otimes n}$ onto the subspace is a pure entangled state. We also show that the purification of entanglement or distillation of entanglement can be carried out by local joint projective measurements with the help of classical communication and local general positive operator valued measurements on a single particle, in principle. Finally we discuss experimental realizability of the entanglement purification.Comment: to appear in PR

Two-qubit controlled-PHASE Rydberg blockade gate protocol for neutral atoms via off-resonant modulated driving within a single pulse

Neutral atom array serves as an ideal platform to study the quantum logic gates, where intense efforts have been devoted to improve the two-qubit gate fidelity. We report our recent findings in constructing a different type of two-qubit controlled-PHASE quantum gate protocol with neutral atoms enabled by Rydberg blockade, which aims at both robustness and high-fidelity. It relies upon modulated driving pulse with specially tailored smooth waveform to gain appropriate phase accumulations for quantum gates. The major features include finishing gate operation within a single pulse, not necessarily requiring individual site addressing, not sensitive to the exact value of blockade shift while suppressing population leakage error and rotation error. We anticipate its fidelity to be reasonably high under realistic considerations for errors such as atomic motion, laser power fluctuation, power imbalance, spontaneous emission and so on. Moreover, we hope that such type of protocol may inspire future improvements in quantum gate designs for other categories of qubit platforms and new applications in other areas of quantum optimal control.Comment: 5 figures, with supplemental materia

Adiabatic Conditions and the Uncertainty Relation

The condition for adiabatic approximation are of basic importance for the applications of the adiabatic theorem. The traditional quantitative condition was found to be necessary but not sufficient, but we do not know its physical meaning and the reason why it is necessary from the physical point of view. In this work, we relate the adiabatic theorem to the uncertainty relation, and present a clear physical picture of the traditional quantitative condition. It is shown that the quantitative condition is just the amplitude of the probability of transition between two levels in the time interval which is of the order of the time uncertainty of the system. We also present a new sufficient condition with clear physical picture.Comment: 5 page

A possible partner state of the Y(2175)Y(2175)

We study the $Y(2175)$ using the method of QCD sum rules. There are two independent $ss\bar s\bar s$ interpolating currents with $J^{PC} = 1^{--}$, and we calculate both their diagonal and off-diagonal correlation functions. We obtain two new currents which do not strongly correlate to each other, so they may couple to two different physical states: one of them couples to the $Y(2175)$, while the other may couple to another state whose mass is about $71 ^{+172}_{-~48}$ MeV larger. Evidences of the latter state can be found in the BaBar, BESII, Belle, and BESIII experiments.Comment: 10 pages, 8 figures, comments and suggestions welcom

Polarization induced interference within electromagnetically induced transparency for atoms of double-V linkage

People have been paying attention to the role of atoms' complex internal level structures in the research of electromagnetically induced transparency (EIT) for a long time, where the various degenerate Zeeman levels usually generate complex linkage patterns for the atomic transitions. It turns out, with special choices of the atomic states and the atomic transitions' linkage structure, clear signatures of quantum interference induced by the probe and coupling light's polarizations can emerge from a typical EIT phenomena. We propose to study a four state system with double-V linkage pattern for the transitions and analyze the polarization induced interference under the EIT condition. We show that such interference arises naturally under mild conditions on the optical field and atom manipulation. Its anticipated properties and its potential application of all optical switching in polarization degree of freedom are also discussed. Moreover, we construct a variation form of double-M linkage pattern where the polarization induced interference enables polarization-dependent cross-modulation between incident lights that can be effective even at the few-photon level. The theme is to gain more insight into the essential question: how can we build non-trivial optical medium where incident lights will induce polarization-dependent non-linear optical interactions, covering a wide range of the incidence intensity from the many-photon level to the few-photon level, respectively.Comment: 7 figure

Analysis of quantum interface between Rydberg-blocked atomic ensemble and cavity optical field with two-photon transition

We study the atom-photon quantum interface with intracavity Rydberg-blocked atomic ensemble where the ground-Rydberg transition is realized by two-photon transition. Via theoretical analysis, we report our recent findings of the Jaynes-Cummings model on optical domain and robust atom-photon quantum gate enabled by this platform. The requirement on the implementation is mild which includes an optical cavity of moderately high finesse, typical alkali atoms such as Rb or Cs and the condition that cold atomic ensemble is well within the Rydberg blockade radius. The analysis focuses on the atomic ensemble's collective coupling to the quantized optical field in the cavity mode. We demonstrate its capability to serve as a controlled-PHASE gate between photonic qubits and matter qubits. The detrimental effects associated with several major decoherence factors of this system are also considered in the analysis.Comment: 11 pages, 8 figure