We consider the exchange of spin and orbital angular momenta between a circularly polarized Laguerre-Gaussian beam of light and a single atom trapped in a two-dimensional harmonic potential. The radiation field is treated classically but the atomic center-of-mass motion is quantized. The spin and orbital angular momenta of the field are individually conserved upon absorption, and this results in the entanglement of the internal and external degrees of freedom of the atom. We suggest applications of this entanglement in quantum information processing.
Simple examples are presented of Lorentz transformations that entangle the spins and momenta of two particles with positive mass and spin 1/2. They apply to indistinguishable particles, produce maximal entanglement from finite Lorentz transformations of states for finite momenta, and describe entanglement of spins produced together with entanglement of momenta. From the entanglements considered, no sum of entanglements is found to be unchanged.
We propose a simple technique to generate entanglement between distant cavities by using entanglement swapping involving atomic momenta. For the proposed scheme, we have two identical atoms, both initially in their ground state, each incident on far apart cavities with particular initial momenta. The two cavities are prepared initially in superposition of zero and one photon state. First, we interact each atom with a cavity in dispersive way. The interaction results into atom-field entangled state. Then we perform EPR state measurement on both atomic momenta state which is an analog of Bell me…
In this paper we explore the entanglement of two relativistic spin-$1/2$ particles with continuous momenta. The spin state is described by the Bell state and the momenta are given by Gaussian distributions of product form. Transformations of the spins are systematically investigated in different boost scenarios by calculating the orbits and concurrence of the spin degree of freedom. By visualizing the behavior of the spin state we get further insight into how and why the entanglement changes in different boost situations.
We study the structure of maps that Lorentz boosts induce on the spin degree of freedom of a system consisting of two massive spin-$1/2$ particles. We consider the case where the spin state is described by the Werner state and the momenta are discrete. Transformations on the spins are systematically investigated in various boost scenarios by calculating the orbit and concurrence of the bipartite spin state with different kinds of product and entangled momenta. We confirm the general conclusion that Lorentz boosts cause non-trivial behavior of bipartite spin entanglement. Visualization of the e…
We study the properties of quantum information and quantum entanglement in moving frames. We show that the entanglement between the spins and the momenta of two particles can be interchanged under a Lorentz transformation, so that a pair of particles that is entangled in spin but not momentum in one reference frame, may, in another frame, be entangled in momentum at the expense of spin-entanglement. Similarly, entanglement between momenta may be transferred to spin under a Lorentz transformation. While spin and momentum entanglement each is not Lorentz invariant, the joint entanglement of the …
We experimentally realize the internal and external entanglement tradeoff, which is a new kind of entanglement monogamy relation different from that usually discussed. Using a source of twin photons, we find that the external entanglement in polarization of twin photons, and the path-polarization internal entanglement of one photon, limit each other. In the extreme case, when the internal state is maximally entangled, the external entanglement must be vanishing, that illustrate entanglement monogamy. Our results of the experiment coincide with the theoretical predictions, and therefore provide…
Einstein-Podolsky-Rosen (EPR) entanglement introduced in 1935 deals with two particles that are entangled in their positions and momenta. Here we report the first experimental demonstration of EPR position-momentum entanglement of narrowband photon pairs generated from cold atoms. By using two-photon quantum ghost imaging and ghost interference, we demonstrate explicitly that the narrowband photon pairs violate the separability criterion, confirming EPR entanglement. We further demonstrate continuous variable EPR steering for positions and momenta of the two photons. Our new source of EPR-enta…
We study the diffraction of two maximally entangled qubits encoded into spatial modes of light with orbital angular momenta $\pm \hbar l_0$, on angular apertures. Exploiting the uncertainty relation between angular position and momentum, we quantify the diffraction-induced entanglement loss, for different $l_0$, as a function of the angular uncertainty $Δϕ$ induced by the apertures. We demonstrate that the degradation of entanglement follows a universal law parametrised by the product $l_0Δϕ$ alone.} {We study the diffraction of two photonic qubits, which are initially maximally entangled in t…
We show a relation between entanglement and correlations of any form. The internal entanglement of a bipartite system, and its correlations with another system, limit each other. A measure of correlations, of any nature, cannot increase under local operations. Examples are the entanglement monotones, the mutual information, that quantifies total correlations, and the Henderson-Vedral measure of classical correlations. External correlations, evaluated by such a measure, set a tight upper bound on the internal entanglement that decreases as they increase, and so does quantum discord.
Single photons with helical phase structures may carry a quantized amount of orbital angular momentum (OAM) and their entanglement is important for quantum information science and fundamental tests of quantum theory. Because there is no theoretical upper limit on how many quanta of OAM a single photon can carry, it is possible to create entanglement between two particles with an arbitrary high difference in the quantum number. By transferring polarization entanglement to OAM with an interferometric scheme, we generate and verify entanglement up to 600 quanta difference in the orbital angular m…
Entanglement and non-separability of momenta and coordinates at colliders
INFN, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；Laboratory of High-Energy and Computational Physics, NICPB（尼古拉斯·伯尔曼物理研究所高能计算物理实验室）；Institute of Computer Science, University of Tartu（塔尔图大学计算机科学研究所）
We predict that if internal and momentum states of an interfering object are correlated (entangled), then by measuring its internal state we may infer both path (corpuscular) and phase (wavelike) information with much higher precision than for objects lacking such entanglement. We thereby partly circumvent the standard complementarity constraints of which-path detection.
Lorentz boosts on particles with spin and momentum degrees of freedom induce momentum-dependent rotations. Since, in general, different particles have different momenta, the transformation on the whole state is not a representation of the rotation group. Here we identify the group that acts on a two-particle system and, for the case when the momenta of the particles are correlated, find invariant subspaces that have interesting properties for quantum information processes in relativistic scenarios. A basis of states is proposed for the study of transformations of spin states under Lorentz boos…
We consider the propagation of two photonic qubits, initially maximally entangled in their orbital angular momenta (OAM), across a turbulent atmosphere. By introducing the {\it phase correlation length} of an OAM beam, we show that the entanglement of OAM photons exhibits a universal exponential decay under turbulence.
Although a precise description of microscopic physical problems requires a full quantum mechanical treatment, physical quantities are generally discussed in terms of classical variables. One exception is quantum entanglement which apparently has no classical counterpart. We demonstrate here how quantum entanglement may be within the de Broglie-Bohm interpretation of quantum mechanics visualized in geometrical terms, giving new insight into this mysterious phenomenon and a language to describe it. On the basis of our analysis of the dynamics of a pair of qubits, quantum entanglement is linked t…
Our investigation aims to study the specific role played by entanglement in the quantum computation process, by elaborating an entangled spin model developed within the 'hidden measurement approach' to quantum mechanics. We show that an arbitrary tensor product state for the entity consisting of two entangled qubits can be described in a complete way by a specific internal constraint between the ray and density states of the two qubits. For the individual qubits we use a sphere model representation, which is a generalization of the Bloch or Pauli representation, where also the collapse and non…
The aim of this paper is to revisit the implications of complementarity when we inject into a Mach Zehnder interferometer particles with internal structure, prepared in special translational-internal entangled (TIE) states. This correlation causes the path distinguishability to be phase dependent in contrast to the standard case. We show that such a TIE state permits us to detect small phase shifts along with almost perfect path distinguishability, beyond the constraints imposed by complementarity on simultaneous which-way and which-phase measurements for standard cases (when distinguishabilit…
We study a system of two entangled spin 1/2, were the spin's are represented by a sphere model developed within the hidden measurement approach which is a generalization of the Bloch sphere representation, such that also the measurements are represented. We show how an arbitrary tensor product state can be described in a complete way by a specific internal constraint between the ray or density states of the two spin 1/2. We derive a geometrical view of entanglement as a 'rotation' and 'stretching' of the sphere representing the states of the second particle as measurements are performed on the…
We propose a scheme for entangling the motional mode of a trapped atom with a propagating light field via a cavity-mediated parametric interaction. We then show that if this light field is subsequently coupled to a second distant atom via a cavity-mediated linear-mixing interaction, it is possible to transfer the entanglement from the light beam to the motional mode of the second atom to create an EPR-type entangled state of the positions and momenta of two distantly-separated atoms.
We evaluate the entanglement entropy of a single connected region in excited states of one-dimensional massive free theories with finite numbers of particles, in the limit of large volume and region length. For this purpose, we use finite-volume form factor expansions of branch-point twist field two-point functions. We find that the additive contribution to the entanglement due to the presence of particles has a simple "qubit" interpretation, and is largely independent of momenta: it only depends on the numbers of groups of particles with equal momenta. We conjecture that at large momenta, the…
In this work we study the entanglement properties under a Lorentz boost of a pair of spin- 1 massive particles, with spin and momentum as the sole degrees of freedom of the system. Different cases for entanglement between spins and momenta are considered as initial states and it is shown that entanglement between the different degrees of freedom is, in general, not invariant. We analyze the entanglement change in terms of the Wigner rotation induced by the transformation and show that, for the case of spin-1 particles, the relative entanglement change between different states depends strongly …
We propose dissociation of cold diatomic molecules as a source of atom pairs with highly correlated (entangled) positions and momenta, approximating the original quantum state introduced by Einstein, Podolsky and Rosen (EPR) [Phys. Rev. 47, 777 (1935)]. Wavepacket teleportation is shown to be achievable by its collision with one of the EPR correlated atoms and manipulation of the other atom in the pair.
Quantum protocols will be more efficient with high-dimensional entangled states. Photons carrying orbital angular momenta can be used to create a high-dimensional entangled state. In this paper we experimentally demonstrate the entanglement of the orbital angular momentum between the Stokes and anti-Stokes photons generated in a hot atomic ensemble using spontaneous four-wave-mixing. This experiment also suggests the existence of the entanglement concerned with spatial degrees of freedom between the hot atomic ensemble and the Stokes photon.
The correlation properties of the pump field in spontaneous parametric down-conversion are crucial in determining the degree of entanglement of generated signal and idler photons. We find theoretically that continuous-variable entanglement of the transverse positions and momenta of these photons can be achieved only if the coherence of the pump beam is sufficiently high. The positions of signal and idler photons are found to be correlated, even for an incoherent pump. However, the momenta of the signal and idler photons are not anti-correlated, even though transverse momentum is conserved.
The monogamy relations of entanglement are highly significant. However, they involve only amounts of entanglement shared by different subsystems. Results on monogamy relations between entanglement and other kinds of correlations, and particularly classical correlations, are very scarce. Here we experimentally observe a tradeoff relation between internal quantum nonseparability and external total correlations in a photonic system and found that even purely classical external correlations have a detrimental effect on internal nonseparability. The nonseparability we consider, measured by the conc…
The entanglement between spins of a pair of particles may change because the spin and momentum become mixed when viewed by a moving observer [R.M. Gingrich and C. Adami, Phys. Rev. Lett. 89, 270402 (2002)]. In this paper, it is shown that, if the momenta are appropriately entangled, the entanglement between the spins of the Bell states can remain maximal when viewed by any moving observer. Further, we suggest a relativistic-invariant protocol for quantum communication, with which the non-relativistic quantum information theory could be invariantly applied to relativistic situations.
We propose a scheme to generate an effective interaction of arbitrary strength between the internal degrees of freedom of two atoms placed in distant cavities connected by an optical fiber. The strength depends on the field intensity in the cavities. As an application of this interaction, we calculate the amount of entanglement it generates between the internal states of the distant atoms. The scheme effectively converts entanglement distribution networks to networks of interacting spins.
We study special relativistic effects on the entanglement between either spins or momenta of composite quantum systems of two spin-1/2 massive particles, either indistinguishable or distinguishable, in inertial reference frames in relative motion. For the case of indistinguishable particles, we consider a balanced scenario where the momenta of the pair are well-defined but not maximally entangled in the rest frame while the spins of the pair are described by a one-parameter ($η$) family of entangled bipartite states. For the case of distinguishable particles, we consider an unbalanced scenario…
Both the topics of entanglement and particle statistics have aroused enormous research interest since the advent of quantum mechanics. Using two pairs of entangled particles we show that indistinguishability enforces a transfer of entanglement from the internal to the spatial degrees of freedom without any interaction between these degrees of freedom. Moreover, sub-ensembles selected by local measurements of the path will in general have different amounts of entanglement in the internal degrees of freedom depending on the statistics (either fermionic or bosonic) of the particles involved.
We propose and study a method for detecting ground-state entanglement in a chain of trapped ions, which realizes a suggested scheme for detecting vacuum entanglement in quantum field theory. We show that the entanglement between single ions or groups of ions can be swapped to the internal levels of two ions by sending laser pulses that couple the internal and motional degrees of freedom. This allows to entangle two ions without actually doing gates. A proof of principle of the effect can be realized with two trapped ions and is feasible with current technology.
We describe and analyse numerically schemes (i) for entangling orthogonal motional modes of one or a few harmonically-trapped atoms or ions, and (ii) for transferring the entanglement from one of these local modes to a distant trapped atom (or atoms) via a light-mediated quantum state transfer procedure proposed in previous work [A.S. Parkins and H.J. Kimble, J. Opt. B: Quantum Semiclass. Opt. 1, 496 (1999)]. Possibilities arising from these schemes include the generation of an Einstein-Podolsky-Rosen state in the positions and momenta of distantly-separated trapped atoms and the preparation o…
We use a microscopic model, the Mirror-Oscillator-Field (MOF) model proposed by Galley, Behunin and Hu [Phys. Rev. A 87, 043832 (2013)], to describe the quantum entanglement between a mirror's center of mass (CoM) motion and a field. In contrast with the conventional approach where the mirror-field entanglement is understood as arising from the radiation pressure of an optical field inducing the motion of the mirror's CoM, the MOF model incorporates the dynamics of the internal degrees of freedom of the mirror that couple to the optical field directly. The major advantage in this approach is t…
Majorana stars, the antipodal directions associated with the coherent states that are orthogonal to a spin state, provide a visualization and a geometric understanding of the structures of general quantum states. For example, the Berry phase of a spin-1/2 is given by half the solid angle enclosed by the close path of its Majorana star. It is conceivable that the Berry phase of higher spins may also be related to the geometry of the Majorana constellation. We find that for a spin-1 state, besides the expected contributions from the solid angles enclosed by the close paths of the two Majorana st…
We propose a method to prepare entangled states and implement quantum computation with atoms in optical cavities. The internal state of the atoms are entangled by a measurement of the phase of light transmitted through the cavity. By repeated measurements an entangled state is created with certainty, and this entanglement can be used to implement gates on qubits which are stored in different internal degrees of freedom of the atoms. This method, based on measurement induced dynamics, has a higher fidelity than schemes making use of controlled unitary dynamics.
We report on our recent progress on the manipulation of single rubidium atoms trapped in optical tweezers and the generation of entanglement between two atoms, each individually trapped in neighboring tweezers. To create an entangled state of two atoms in their ground states, we make use of the Rydberg blockade mechanism. The degree of entanglement is measured using global rotations of the internal states of both atoms. Such internal state rotations on a single atom are demonstrated with a high fidelity.
We show that macroscopic thermodynamical properties - such as functions of internal energy and magnetization - can detect quantum entanglement in solids at nonzero temperatures in the thermodynamical limit. We identify the parameter regions (critical values of magnetic field and temperature) within which entanglement is witnessed by these thermodynamical quantities.
With quantum interference of two-path spontaneous emissions, we propose a novel scheme to coherently control the atom--photon momentum entanglement through atomic internal coherence. A novel phenomenon called ``momentum phase entanglement'' is reported, and we found, under certain conditions, that more controllable entangled state can be produced with super--high degree of entanglement.
The properties of the entanglement entropy (EE) of two particle excited states in a one-dimensional ring are studied. For a clean system we show analytically that as long as the momenta of the two particles are not close, the EE is twice the value of the EE of any single particle state. For almost identical momenta the EE is lower than this value. The introduction of disorder is numerically shown to lead to a decrease in the median EE of a two particle excited state, while interactions (which have no effect for the clean case) mitigate the decrease. For a ring which is of the same size as the …
We investigate entanglement of solitons in the continuum-limit of the nonlinear Frenkel-Kontorova chain. We find that the entanglement of solitons manifests particle-like behavior as they are characterized by localization of entanglement. The von-Neumann entropy of solitons mixes critical with noncritical behaviors. Inside the core of the soliton the logarithmic increase of the entropy is faster than the universal increase of a critical field, whereas outside the core the entropy decreases and saturates the constant value of the corresponding massive noncritical field. In addition, two soliton…
Recently, interest has increased in the entanglement of remote quantum particles through the Newtonian gravitational interaction, both from a fundamental perspective and as a test case for the quantization of gravity. Likewise, post-Newtonian gravitational effects in composite nonrelativistic quantum systems have been discussed, where the internal energy contributes to the mass, promoting the mass to a Hilbert space operator. Employing a modified version of a previously considered thought experiment, it can be shown that both concepts, when combined, result in inconsistencies, reinforcing the …
We compute the entanglement entropy variation between initial (separable or entangled in the momenta) and final states $ΔS_E$ in an elastic scattering of a bipartite system composed by two interacting scalar particles. We perform a quantum field theoretical calculation to one loop order and verify that $ΔS_E $ changes as we vary the energy of incoming particles and the coupling strength in a non-trivial way.
We explore spin-orbit thermal entanglement in rare-earth ions, based on a witness obtained from mean energies. The entanglement temperature $T_{E}$, below which entanglement emerges, is found to be thousands of kelvin above room temperature for all light rare earths. This demonstrate the robustness to environmental fluctuations of entanglement between internal degrees of freedom of a single ion.
Two entangled electron spins, or qubits, are analyzed in terms of ordinary three-dimensional space geometric properties, as are the angles between their angular momenta. This formulation allows concurrence, a measure of quantum entanglement, to be expressed as expectation values of trigonometric functions of the azimuthal angle between the two angular momenta.
We address the dynamics induced by collective atomic recoil in a Bose-Einstein condensate in presence of radiation losses and atomic decoherence. In particular, we focus on the linear regime of the lasing mechanism, and analyze the effects of losses and decoherence on the generation of entanglement. The dynamics is that of three bosons, two atomic modes interacting with a single-mode radiation field, coupled with a bath of oscillators. The resulting three-mode dissipative Master equation is solved analytically in terms of the Wigner function. We examine in details the two complementary limits …
In this work we examine the entanglement of the output signal-idler squeezed vacuum state in the Heisenberg picture as a function of the coupling and internal propagation loss parameters of a microring resonator. Using the log-negativity as a measure of entanglement for a mixed Gaussian state, we examine the competitive effects of the transfer matrix that encodes the classical phenomenological loss, as well as the matrix that that incorporates the coupling and internal propagation loss due to the quantum Langevin noise fields required to preserve unitarity of the composite system,(signal-idler…
Entanglement between two electrons belonging to an auto-ionization system and a neighbor two-level atom produced by the dipole-dipole interaction is studied. The entanglement is quantified using the quadratic negativity of a bipartite system including the continuum of states. Suitable conditions for the generation of highly entangled states of two electrons are revealed. Internal structure of the entanglement is elucidated using the spectral density of quadratic negativity.
Entanglement-based technologies, such as quantum information processing, quantum simulations, and quantum-enhanced metrology, have the potential to revolutionise our way of computing and measuring and help clarifying the puzzling concept of entanglement itself. Ultracold atoms on atom chips are attractive for their implementation, as they provide control over quantum systems in compact, robust, and scalable setups. An important tool in this system is a potential depending on the internal atomic state. Coherent dynamics in this potential combined with collisional interactions allows entanglemen…
We study entanglement between quantum states of multi level spin system of a single particle considering a nucleus with spin 3/2 in both the internal electric field gradient and the external magnetic field. It was shown that entanglement is achieved by applying a magnetic field to a single particle at low temperature (~ 5 mK). In this temperature range, the numerical calculation revealed the coincidence between magnetization and concurrence. As a result, the magnetization can be used as an entanglement witness for such systems.
This paper was concerned with the spin-momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only two momentum eigen states (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin-momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not observer-dependent quantity in inertial …
