Entangled Wave Research Articles

Characteristics of Entanglement Wave in Two Parallel Spin Chains

Based on the solvable spin-1/2 Heisenberg chain we demonstrate how two many-body systems are entangled due to their partial entanglement. The entanglement wave in the two spin chains displays a damped oscillation if the spin number is N > 3, and only propagates with a certain velocity depending on the coupling constant J. Moreover, the entanglement wave will be reflected on the other ends of the two spin chains. A simple scheme for transferring some special two-qubit states to other two distant qubits is also proposed.

Entanglement spectrum of composite fermion states in real space

We study the entanglement spectra of many particle systems in states which are closely related to products of Slater determinants or products of permanents, or combinations of the two. Such states notably include the Laughlin and Jain composite fermion states which describe most of the observed conductance plateaus of the fractional quantum Hall effect. We identify a set of 'Entanglement Wave Functions' (EWF), for subsets of the particles, which completely describe the entanglement spectra of such product wave functions, both in real space and in particle space. A subset of the EWF for the Laughlin and Jain states can be recognized as Composite Fermion states. These states provide an exact description of the low angular momentum sectors of the real space entanglement spectrum (RSES) of these trial wave functions and a physical explanation of the branches of excitations observed in the RSES of the Jain states.

Steady-State Many-Body Entanglement of Hot Reactive Fermions

Entanglement is typically created via systematic intervention in the time evolution of an initially unentangled state, which can be achieved by coherent control, carefully tailored nondemolition measurements, or dissipation in the presence of properly engineered reservoirs. In this Letter we show that two-component Fermi gases at ~μK temperatures naturally evolve, in the presence of reactive two-body collisions, into states with highly entangled (Dicke-type) spin wave functions. The entanglement is a steady-state property that emerges-without any intervention-from uncorrelated initial states, and could be used to improve the accuracy of spectroscopy in experiments with fermionic alkaline earth atoms or fermionic ground state molecules.

Observing the Phase Space Trajectory of an Entangled Matter Wave Packet

We observe the phase space trajectory of an entangled wave packet of a trapped ion with high precision. The application of a spin-dependent light force on a superposition of spin states allows for coherent splitting of the matter wave packet such that two distinct components in phase space emerge. We observe such motion with a precision of better than 9% of the wave packet extension in both momentum and position, corresponding to a 0.8 nm position resolution. We accurately study the effect of the initial ion temperature on the quantum entanglement dynamics. Furthermore, we map out the phonon distributions throughout the action of the displacement force. Our investigation shows corrections to simplified models of the system evolution. The precise knowledge of these dynamics may improve quantum gates for ion crystals and lead to entangled matter wave states with large displacements.

Amplitude and phase modulation of time-energy entangled two-photon states

We experimentally demonstrate amplitude and phase modulation of a time-energy entangled two-photon wave function. The entangled photons are produced by spontaneous parametric down-conversion, spectrally dispersed in an prism compressor, modulated in amplitude and/or phase, and detected in coincidence by sum-frequency generation. First, we present a Fourier optical analysis of the optical setup yielding an analytic expression for the resulting field distribution at the exit plane of the shaping apparatus. We then introduce amplitude and/or phase shaping and present results which can only be obtained through a combination of the two. Specifically, we use a shaper-based interferometer to measure the two-photon interference of an almost bandwidth-limited two-photon wave function.

Short-pulse or strong-field breakup processes: a route to study entangled wave packets

Strong and/or short laser pulses provide one avenue for rapid separation of composite quantum systems. Daughter particles can exhibit subtle aspects of quantum entanglement. We show that a Gaussian approximation provides a unifying overview of rapidly separating systems in many contexts, and propose using combined single-particle and coincidence measurements of wave-packet widths of bipartite systems for experimental observation of the degree of entanglement.

Generation of entangled lights with temporally reversed photon wave packets

We theoretically study the control of a weak quantum light in a resonant three-level condensed medium derived by a pair of resonant counterpropagating laser fields. We analytically demonstrate that the adiabatic switching on of one of the control fields generates an entangled state of photon wave packets moving together at subnormal slow velocity in the medium with relative amplitudes determined by the control laser fields. An abrupt switching-off the control field makes the entangled wave packets propagate in the opposite direction with temporally reversed profiles relative to each other. We have analyzed the quantum control of the entanglement generation in terms of the adiabatic and nonadiabatic switching operations of the coupling laser pulse.

On extremal quantum states of composite systems with fixed marginals

We study the convex set C(ρ1,ρ2) of all bipartite quantum states with fixed marginal states ρ1 and ρ2. The extremal states in this set have recently been characterized by Parthasarathy [Ann. Henri Poincaré (to appear), quant-ph/0307182]. Here we present an alternative necessary and sufficient condition for a state in C(ρ1,ρ2) to be extremal. Our approach is based on a canonical duality between bipartite states and a certain class of completely positive maps and has the advantage that it is easier to check and to construct explicit examples of extremal states. In dimension 2×2 we give a simple new proof for the fact that all extremal states in C(121,121) are precisely the projectors onto maximally entangled wave functions. We also prove that in higher dimension this does not hold and construct an explicit example of an extremal state in C(131,131) that is not maximally entangled. Generalizations of this result to higher dimensions are also discussed.

Real-time evolution using the density matrix renormalization group.

We describe an extension to the density matrix renormalization group method incorporating real-time evolution. Its application to transport problems in systems out of equilibrium and frequency dependent correlation functions is discussed and illustrated in several examples. We simulate a scattering process in a spin chain which generates a spatially nonlocal entangled wave function.

Dynamics of entanglement in one-dimensional spin systems

We study the dynamics of quantum correlations in a class of exactly solvable Ising-type models. We analyze in particular the time evolution of initial Bell states created in a fully polarized background and on the ground state. We find that the pairwise entanglement propagates with a velocity proportional to the reduced interaction for all the four Bell states. Singlet-like states are favored during the propagation, in the sense that triplet-like states change their character during the propagation under certain circumstances. Characteristic for the anisotropic models is the instantaneous creation of pairwise entanglement from a fully polarized state; furthermore, the propagation of pairwise entanglement is suppressed in favor of a creation of different types of entanglement. The ``entanglement wave'' evolving from a Bell state on the ground state turns out to be very localized in space-time. Further support to a recently formulated conjecture on entanglement sharing is given.

Role of locality in Einstein-Podolsky-Rosen correlations and teleportation

Two-body systems with pure entangled wave functions are known not to satisfy local realism; that is, they display nonlocality. However, it is noted that the well-known conclusion of the EPR paradox that quantum mechanics is an incomplete theory is inconclusive, and that local quantum-mechanical calculations are sufficient to explain two-body correlations. Such correlations are commonly attributed to an instant nonlocal interaction, but that is neither required nor observable in a two-body system. However, nonlocal transmission could be directly detected in sequential three-body processes, and a test for this is proposed by the direct timing of the teleportation of a wave function. The result of this would help towards establishing a dynamical theory of teleportation.

Entangled two-photon wave packet in a dispersive medium.

We report an experimental study of group-velocity dispersion effect on an entangled two-photon wave packet, generated via spontaneous parametric down-conversion and propagating through a dispersive medium. Even in the case of using cw laser beam for pump, the biphoton wave packet and the second-order correlation function spread significantly. The study and understanding of this phenomenon is of great importance for quantum information applications, such as quantum communication and distant clock synchronization.

Uncertainty relations for entangled states

A generalized uncertainty relation for an entangled pair of particles is obtained if we impose a symmetrization rule for all operators that we should employ when doing any calculation using the entangled wave function of the pair. This new relation reduces to Heisenberg’s uncertainty relation when the particles have no correlation and suggests that we can have new lower bounds for the product of position and momentum dispersions.

Optical Wigner functions for two-photon entangled wave packets

Einstein–Podolsky–Rosen (EPR) correlations produced for two-photon entangled wave packets are analyzed by use of optical Wigner functions. In particular, type-II optical parametric downconversion systems are used, and the effects of the length of the crystal and the filter bandwidth on the Wigner functions are studied. The relation between the optical Wigner functions and the interference experiment with a beam splitter is studied. We find that, whereas in first-order correlation experiments (typified, for example, by Young’s interference experiment) the “photon interferes with itself” [ P. A. M. Dirac , The Principles of Quantum Mechanics (Clarendon, Oxford, UK, 1958), p. 9], in the EPR correlations the two-photon amplitude function interferes with itself. Such interference is analyzed by use of the optical Wigner functions.

Geometry of the Schmidt decomposition and Hardy’s theorem

The Schmidt decomposition theorem allows us to express an entangled wave function of two quantum systems in a particularly simple form. The purpose of this paper is to describe a geometrical method of performing the Schmidt decomposition that complements the usual algebraic method. This geometrical method is worked out in detail for a pair of spin-1/2 particles and its utility is illustrated by giving a simple discussion of several aspects of Hardy’s version of Bell’s theorem.