Universal geometric entanglement close to quantum phase transitions

Under successive renormalization group transformations applied to a quantum state |Psi of finite correlation length xi, there is typically a loss of entanglement after each iteration. How good it is then to replace |Psi by a product state at every step of the process? In this Letter we give a quantitative answer to this question by providing first analytical and general proofs that, for translationally invariant quantum systems in one spatial dimension, the global geometric entanglement per region of size L>xi diverges with the correlation length as (c/12)log(xi/epsilon) close to a quantum critical point with central charge c, where is a cutoff at short distances. Moreover, the situation at criticality is also discussed and an upper bound on the critical global geometric entanglement is provided in terms of a logarithmic function of L.     

Preservation of energy-time entanglement in a slow light medium

We demonstrate the preservation of entanglement of an energy-time entangled biphoton through a slow light medium. Using the D(1) and D(2) fine structure resonances of Rubidium, we delay one photon of the 1.5 THz biphoton by approximately 1.3 correlation lengths and measure the fourth order correlation fringes. After the group delay the fringe visibility is reduced from 97.0+/-4.4% to 80.0+/-4.8%, but is still sufficient to violate a Bell inequality. We show that temporal broadening is the primary mechanism for reducing the fringe visibility and that smaller bandwidths lead to greatly reduced broadening.     

Proposal for energy-time entanglement of quasiparticles in a solid-state device

We present a proposal for the experimental observation of energy-time entanglement of quasiparticles in mesoscopic physics. This type of entanglement arises whenever correlated particles are produced at the same time and this time is uncertain in the sense of quantum uncertainty, as has been largely used in photonics. We discuss its feasibility for electron-hole pairs. In particular, we argue that junctions between materials in which electrons and holes, respectively, propagate ballistically and behave as "entanglers" for energy-time entanglement when irradiated with a continuous laser.     

Pairwise entanglement and geometric phase in high dimensional free-Fermion lattice systems

The pairwise entanglement, measured by concurrence and geometric phase in high dimensional free-Fermion lattice systems have been studied in this paper. When the system stays at the ground state, their derivatives with the external parameter show the singularity closed to the phase transition points, and can be used to detect the phase transition in this model. Furthermore our studies show for the free-Fermion model that both concurrence and geometric phase show the intimate connection with the correlation functions. The possible connection between concurrence and geometric phase has been also discussed.     

Global geometric entanglement and quantum phase transition in three-leg spin-3/2 Heisenberg tubes

Based on the tensor network representations, we have developed an efficient scheme to calculate the global geometric entanglement as a multipartite entanglement measure for the three-leg spin tubes. From the geometric entanglement, the phase diagram of a spin-3 / 2 isosceles triangle spin tube has been investigated varying the base interaction α. Two Berezinsky-Kosterlitz-Thouless phase transitions are estimated to be α_c1 ? 0.68 and α_c2 ? 3.85, respectively. Then, even though the spin tube is in gapless spin liquid phases for α<α_c1 and α >α_c2, the geometrical structure difference between the groundstate wavefunctions for the two regions is found to reflect the global geometric entanglement that contains bipartite and multipartite contributions. Further, the phase transition points from the von Neumann entropies and fidelity are consistent with that from the geometric entanglement. As a result, the global geometric entanglement can be used to explore a geometrical nature of quantum phases as well as an indicator for quantum phase transitions in many-body lattice systems.     

Fiber-optic tunable loop mirror using Berry's geometric phase

A method is presented for constructing a fiber-optic loop mirror whose reflectivity is tunable even though a fixed-ratio directional coupler is used. The tunability is polarization and wavelength independent and depends only on the geometry of the fiber-tuning element. This loop mirror can be used to transfer energy from one channel to another in a controllable way. We experimentally demonstrate the tunable reflectivity and present some experimental investigations.     

Polarization entanglement purification using spatial entanglement

We present a scheme for entanglement purification with linear optics that works for currently available parametric down-conversion sources, in contrast to a previous scheme [J. W. Pan, Nature (London) 410, 1067 (2001)]] that relied on ideal single-pair sources. The present scheme makes use of spatial entanglement in order to purify polarization entanglement. Surprisingly, spatial entanglement as an additional resource also leads to a substantial improvement in entanglement output compared to the previous scheme.     

Large-alphabet quantum key distribution using energy-time entangled bipartite States

We present a protocol for large-alphabet quantum key distribution (QKD) using energy-time entangled biphotons. Binned, high-resolution timing measurements are used to generate a large-alphabet key with over 10 bits of information per photon pair, albeit with large noise. QKD with 5% bit error rate is demonstrated with 4 bits of information per photon pair, where the security of the quantum channel is determined by the visibility of Franson interference fringes. The protocol is easily generalizable to even larger alphabets, and utilizes energy-time entanglement which is robust to transmission over large distances in fiber.     

Quantum phase control of entanglement

A method of phase control of entanglement in two-qubit systems is proposed. We show that by changing a relative phase of the pulses that drive the transitions in a two-qubit system with closed-loop couplings, one can control entanglement at will. The method relies on adiabatic dynamics via time-delayed pulse sequences and can be implemented with both resonant and nonresonant transitions.     

Quantum cryptography using entangled photons in energy-time bell states

We present a setup for quantum cryptography based on photon pairs in energy-time Bell states and show its feasibility in a laboratory experiment. Our scheme combines the advantages of using photon pairs instead of faint laser pulses and the possibility to preserve energy-time entanglement over long distances. Moreover, using four-dimensional energy-time states, no fast random change of bases is required in our setup: Nature itself decides whether to measure in the energy or in the time base, thus rendering eavesdropper attacks based on "photon number splitting" less efficient.     

相位阻尼通道下初始纠缠对纠缠演化的影响

研究了在非惯性系中相位阻尼通道下初始纠缠对纠缠演化的影响.结果发现:与振幅阻尼通道情况不同,当态参数不同而初始纠缠相同时,纠缠演化曲线重合.当Unruh单粒子态包含左右成分时,比只包含右成分时量子消相干现象更加严重,较早地出现了纠缠死亡现象,并且纠缠死亡时刻与初始纠缠无关.     

Quantum phase transitions and bipartite entanglement

We develop a general theory of the relation between quantum phase transitions (QPTs) characterized by nonanalyticities in the energy and bipartite entanglement. We derive a functional relation between the matrix elements of two-particle reduced density matrices and the eigenvalues of general two-body Hamiltonians of d-level systems. The ground state energy eigenvalue and its derivatives, whose nonanalyticity characterizes a QPT, are directly tied to bipartite entanglement measures. We show that first-order QPTs are signaled by density matrix elements themselves and second-order QPTs by the first derivative of density matrix elements. Our general conclusions are illustrated via several quantum spin models.     

Measurement of geometric phase for mixed states using single photon interferometry

Geometric phase may enable inherently fault-tolerant quantum computation. However, due to potential decoherence effects, it is important to understand how such phases arise for mixed input states. We report the first experiment to measure mixed-state geometric phases in optics, using a Mach-Zehnder interferometer, and polarization mixed states that are produced in two different ways: decohering pure states with birefringent elements; and producing a nonmaximally entangled state of two photons and tracing over one of them, a form of remote state preparation.     

Two-photon coincident-frequency entanglement via extended phase matching

We demonstrate a new class of frequency-entangled states generated via spontaneous parametric down-conversion under extended phase-matching conditions. Biphoton entanglement with coincident signal and idler frequencies is observed over a broad bandwidth in periodically poled KTiOPO4. We demonstrate high visibility in Hong-Ou-Mandel interferometric measurements under pulsed pumping without spectral filtering, which indicates excellent frequency indistinguishability between the down-converted photons. The coincident-frequency entanglement source is useful for quantum information processing and quantum measurement applications.     

A millimeter-wave geometric phase interferometer

A millimeter-wave interferometer operating purely on the geometric phase is presented. Like its optical counterpart described by Hariharan and Roy, this system uses two circular polarizers with a half-wave section in between. The geometric phase of each signal is determined by the orientation of the half-wave section.     

Multipartite entanglement signature of quantum phase transitions

We derive a general relation between the nonanalyticities of the ground state energy and those of a subclass of the multipartite generalized global entanglement (GGE) measure defined by de Oliveira et al. [Phys. Rev. A 73, 010305(R) (2006)] for many-particle systems. We show that GGE signals both a critical point location and the order of a quantum phase transition (QPT). We also show that GGE allows us to study the relation between multipartite entanglement and QPTs, suggesting that multipartite but not bipartite entanglement is favored at the critical point. Finally, using GGE we were able, at a second-order QPT, to define a diverging entanglement length (EL) in terms of the usual correlation length. We exemplify this with the XY spin-1/2 chain and show that the EL is half the correlation length.     

Effects of quantum entanglement in phase transitions

Starting with the canonical ensemble over the space of pure quantum states, we obtain an integral representation for the associated partition function. This is used to calculate the magnetisation of a system of N spin- particles. The results suggest the existence of a first order phase transition that occurs at zero temperature in the absence of spin-spin interactions.     

Modeling and computation of two phase geometric biomembranes using surface finite elements

Biomembranes consisting of multiple lipids may involve phase separation phenomena leading to coexisting domains of different lipid compositions. The modeling of such biomembranes involves an elastic or bending energy together with a line energy associated with the phase interfaces. This leads to a free boundary problem for the phase interface on the unknown equilibrium surface which minimizes an energy functional subject to volume and area constraints. In this paper we propose a new computational tool for computing equilibria based on an L² relaxation flow for the total energy in which the line energy is approximated by a surface Ginzburg–Landau phase field functional. The relaxation dynamics couple a nonlinear fourth order geometric evolution equation of Willmore flow type for the membrane with a surface Allen–Cahn equation describing the lateral decomposition. A novel system is derived involving second order elliptic operators where the field variables are the positions of material points of the surface, the mean curvature vector and the surface phase field function. The resulting variational formulation uses H¹ spaces, and we employ triangulated surfaces and H¹ conforming quadratic surface finite elements for approximating solutions. Together with a semi-implicit time discretization of the evolution equations an iterative scheme is obtained essentially requiring linear solvers only. Numerical experiments are presented which exhibit convergence and the power of this new method for two component geometric biomembranes by computing equilibria such as dumbbells, discocytes and starfishes with lateral phase separation.     

Possible gravitational radiation detection using the geometric phase of a light beam

An effect of geometrical phase shift is predicted for a light beam propagating in the field of a gravitational wave. For the beam travelling orthogonally to the direction of propagation of the gravitational wave from an observer and returning back after being reflected, this phase is shown to grow proportionally toL/ whereL is the distance between the observer and reflecting system, and the characteristic wavelength of the gravitational wave packet (for light propagating parallel or antiparallel to the gravitational wave, the geometric phase shift is absent). Gravitational radiation detection experiments are proposed using this new effect, the corresponding estimates being given.On leave of absence from: Peoples' Friendship University, Moscow, RussiaOn leave of absence from: Krasnoyarsk State University, Krasnoyarsk, Russia     

Measuring entanglement using quantum quenches

We show that block entanglement entropies in one-dimensional systems close to a quantum critical point can, in principle, be measured in terms of the population of low-lying energy levels following a certain type of local quantum quench.