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arXiv:quant-ph/0604165 · Physical Review A

Entanglement of orbital angular momentum states between an ensemble of cold atoms and a photon

Ryotaro Inoue, Nobuhiro Kanai, T. Yonehara, Y. Miyamoto, Masato Koashi, Mikio Kozuma

Published Nov 15, 2006• 85 citations
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Abstract

Recently, atomic ensemble and single photons were successfully entangled by using collective enhancement [D. N. Matsukevich et al., Phys. Rev. Lett. 95, 040405 (2005)], where atomic internal states and photonic polarization states were correlated in a nonlocal manner. Here, we experimentally clarified that in an ensemble of atoms and a photon system, there also exists an entanglement concerned with spatial degrees of freedom. Generation of higher-dimensional entanglement between remote atomic ensemble and an application to condensed matter physics are also discussed.

DOI
10.1103/physreva.74.053809

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Recently, atomic ensemble and single photons were successfully entangled by using collective enhancement [D. N. Matsukevich et al., Phys. Rev. Lett. 95, 040405 (2005)], where atomic internal states and photonic polarization states were correlated in a nonlocal manner. Here, we experimentally clarified that in an ensemble of atoms and a photon system, there also exists an entanglement concerned with spatial degrees of freedom. Generation of higher-dimensional entanglement between remote atomic ensemble and an application to condensed matter physics are also discussed.
The generation of paired photons entangled in the spatial degree of freedom, i.e., in orbital angular momentum, offers a convenient physical resource to investigate the nature of entanglement in a multidimensional Hilbert space with controllable dimensionality. The two main physical processes that generate pairs of photons which show correlations in orbital angular momentum are (a) spontaneous parametric down-conversion (SPDC), and (b) Raman transitions induced in atomic ensembles. One question naturally arises: what kinds of correlations exist between the orbital angular momentum of the generated photons? The answer might be different if we consider the whole quantum state of the generated photons, i.e., all possible directions where the pairs of photons can be emitted, or if we consider only a small section of the full set of directions.
In this paper, we experimentally demonstrate that the photon pairs generated via spontaneous four-wave mixing in a hot atomic ensemble are in entangled orbital angular momentum (OAM) states. The density matrix of the OAM states of the photon pair is reconstructed, from which the fidelity to the maximal entangled state and the concurrence are estimated to be about 0.89 and 0.81, respectively. The experimental result also suggests the existence of the entanglement concerned with spatial degrees of freedom between the hot atomic ensemble and the Stokes photon.
Introduction In this chapter, we will be concerned with entangled states of light. Historically, quantum states of light, i.e., photons, have played a dominant role in the experimental study of quantum entanglement. For instance, the first Bell tests and the first realizations of quantum teleportation were performed using two-dimensional polarization-entangled twophoton states [3]. From an experimental point of view these states are readily prepared and manipulated using conventional polarization optics. Recently, however, both theoretical and experimental efforts have shifted towards entanglement in more than two modes , which is often referred to as high-dimensional entanglement. This is much richer than two-dimensional entanglement, as is, for instance, reflected in stronger violations of various measures of nonlocality which reveal the complexity of high-dimensional Hilbert spaces [4–7]. Also, from an applications perspective, it promises a larger channel capacity [8, 9] and improved security for quantum communication [10, 11]. There are several ways to implement high-dimensional two-photon entanglement. One can exploit the temporal [12], frequency [13], or spatial [14–18] degrees of freedom of the optical field. A promising way to implement high-dimensional two-photon entanglement is to use the orbital-angular-momentum (OAM) degree of freedom of light. Light beams that carry OAM have a helical wavefront that spirals around the optical axis during propagation [19]. The winding number m , which characterizes the OAM eigenmodes, can adopt any integer value between −∞ and ∞; since all coaxial OAM modes are orthogonal they can thus span a very high-dimensional Hilbert space.
Correlated light generated from atomic ensembles can have a central role in prominent quantum information protocols, such as long-distance quantum communication. Here we present our studies on three topics involving the generation of correlated light with four-wave mixing (FWM) in a cold atomic ensemble for applications in quantum communications with high capacity. We experimentally investigate the generation of light with seeded FWM in cold cesium atoms and the time correlations of photon pairs generated with spontaneous FWM. We theoretically investigate the correlations in orbital angular momentum of photon pairs generated with spontaneous FWM for a range of experimental geometries. These studies represent foundational work toward the control and measurement of high-dimensional entanglement in the orbital angular momentum degree of freedom photon pairs for use in high-dimensional quantum communication.
Entanglement between a single photon and a matter qubit is an indispensable resource for quantum repeater and quantum networks. With atomic ensembles, the entanglement creation probability is typically very low to inhibit high-order events. In this paper, we propose and experimentally realize a scheme that creates atom-photon entanglement with an intrinsic efficiency of 50%. We make use of Rydberg blockade to generate two collective excitations, lying in separate internal states. By introducing the momentum degree of freedom for the excitations, and interfering them via Raman coupling, we entangle the two excitations. Via retrieving one excitation, we create the entanglement between the polarization of a single photon and the momentum of the remaining atomic excitation, with a measured fidelity of 0.901(8). The retrieved optical field is verified to be genuine single photons. The realized entanglement may be employed to create entanglement between two distant nodes in a fully heralded way and with a much higher efficiency.
Controlling the orbital angular momentum state opens the door to the manipulation of arbitrarily large dimensional quantum state. Here we propose a new method to estimate the Schmidt number of the quantum state. The method enables us to avoid a problem appearing when we estimate the entanglement on the orbital angular momentum of photons using phase holograms. We also report the experimental results on the atoms-photon entanglement which was analyzed by the proposed method. Our experimental results show the possibility of controlling and entangling two remote massive atoms with higher dimensional basis.