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Physical Review A

Multiple beam splitter for single photons

Tun Wang, Marijan Koštrun, Susanne F. Yelin

Published Nov 24, 2004• 41 citations
Publisher

Abstract

We propose a method using ``light storage'' and fractional stimulated Raman adiabatic passage (F-STIRAP) to get entangled multiple Fock states from a single photon. A light storage technique is used to store the quantum information of a single-photon pulse in atoms. F-STIRAP pulses then split the stored coherence, such that reading pulses retrieve the quantum information from this new coherence. Since each reading pulse only retrieves part of the total coherence, we can obtain entangled multiple Fock states with arbitrary relative amplitude. This method to create entanglement is versatile for obtaining frequency, time, and∕or spatial entanglement. Indeed, we obtain a multiple beam splitter with easily adjustable parameters.

DOI
10.1103/physreva.70.053822

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We propose a method using ``light storage'' and fractional stimulated Raman adiabatic passage (F-STIRAP) to get entangled multiple Fock states from a single photon. A light storage technique is used to store the quantum information of a single-photon pulse in atoms. F-STIRAP pulses then split the stored coherence, such that reading pulses retrieve the quantum information from this new coherence. Since each reading pulse only retrieves part of the total coherence, we can obtain entangled multiple Fock states with arbitrary relative amplitude. This method to create entanglement is versatile for obtaining frequency, time, and∕or spatial entanglement. Indeed, we obtain a multiple beam splitter with easily adjustable parameters.
We discuss a simple scheme for preparing atoms and molecules in an arbitrary preselected coherent superposition of quantum states. The technique, which we call fractional stimulated Raman adiabatic passage ({\it f-STIRAP}), is based upon (incomplete) adiabatic population transfer between an initial state ψ1ψ_1ψ1​ and state ψ3ψ_3ψ3​ through an intermediate state ψ2ψ_2ψ2​. As in STIRAP, the Stokes pulse arrives before the pump pulse, but unlike STIRAP, the two pulses terminate simultaneously while maintaining a constant ratio of amplitudes. The independence of f-STIRAP from details of pulse shape and pulse area makes it the analog of conventional STIRAP in the creation of coherent superpositions of states. We suggest a smooth realization of f-STIRAP which requires only two laser pulses (which can be derived from a single laser) and at the same time ensures the automatic fulfillment of the asymptotic conditions at early and late times. Furthermore, we provide simple analytic estimates of the robustness of f-STIRAP against variations in the pulse intensity, the pulse delay, and the intermediate-state detuning, and discuss its possible extension to multistate systems.
We discuss the properties of a simple and robust scheme for preparing atoms and molecules in an arbitrary preselected coherent superposition of quantum states - fractional stimulated Raman adiabatic passage (fractional STIRAP) - first proposed by Marte et al (1991 Phys. Rev. A 44 R4118). As in STIRAP, the Stokes pulse arrives before the pump pulse, but unlike STIRAP, here the two pulses terminate simultaneously, while maintaining a constant ratio of amplitudes. We extend earlier research and suggest a realization of this scheme with two smoothly varying delayed laser pulses (which can be derived from a single laser), the parameters of the created superposition being controlled by the polarization of the delayed pulse. Furthermore, we provide simple analytic estimates of the robustness of this process against variations in the laser intensity, laser frequency and pulse delay. Finally, we discuss an extension to multistate systems which provides a possibility for creating coherent superpositions of more than two states.
We report the demonstration of a configurable coherent quantum-memory-based beam splitter (BS) for a single-photon wave packet making use of laser-cooled 85Rb^{85}\mathrm{Rb}85Rb atoms and electromagnetically induced transparency. The single-photon wave packet is converted (stored) into a collective atomic spin state and later retrieved (split) into two nearly opposing directions. The storage time, beam-splitting ratio, and relative phase are configurable and can be dynamically controlled. We experimentally confirm that such a BS preserves the quantum particle nature of the single photon and the coherence between the two split wave packets of the single photon.
We demonstrate a coherent and dynamic beam splitter based on light storage in cold atoms. An input weak laser pulse is first stored in a cold atom ensemble via electromagnetically-induced transparency (EIT). A set of counter-propagating control fields, applied at a later time, retrieves the stored pulse into two output spatial modes. The high visibility interference between the two output pulses clearly demonstrates that the beam splitting process is coherent. Furthermore, by manipulating the control lasers, it is possible to dynamically control the storage time, the power splitting ratio, the relative phase, and the optical frequencies of the output pulses. With further improvements, the active beam splitter demonstrated in this work might have applications in photonic photonic quantum information and in all-optical information processing.
We describe a technique for creating superpositions of degenerate quantum states, such as are needed for beam splitters used in matter-wave optics, by manipulating the timing of three orthogonally polarized laser beams through which moving atoms (or molecules) pass; motion across the laser beams produces pulses in the atomic rest frame. As illustrated with representative simulations for transitions in metastable neon, a single pass through three overlapping laser beams can produce superpositions (with preselected phase) of atomic beams differing by transverse momentum corresponding to the momentum of four photons. Like the two-photon momentum transfer of the tripod linkage pattern which it extends, the method relies on controlled adiabatic time evolution in the Hilbert subspace of two degenerate dark states. It is thus a generalization to multiple dark states (and larger transfers of linear momentum to the atomic beam) of the single dark state occurring with the stimulated Raman adiabatic passage (STIRAP) technique, and therefore it is potentially insensitive to decoherence due to spontaneous emission. By extending the tripod-linkage system to more numerous degenerate states, the technique not only increases the atomic beam deflections but, as we demonstrate, allows control over the superposition phase and amplitudes. LIke other techniques based on adiabatic time evolution, the technique is robust with respect to variations of the intensity, timing, and other characteristics of the laser fields. Unlike STIRAP, the same robust partial population transfer occurs for opposite timings of the pulse sequence, as is needed for such procedures as Hadamard gates.
Quantum optomechanical STIRAP (Stimulated Raman Adiabatic Passage) is investigated for a system of two mechanical modes coupled to an optical mode. We show analytically that in a system without loss, fractional STIRAP can generate a mechanical Bell state from a single phonon Fock state of one of the mechanical modes with the other mechanical mode in the vacuum state, and a product state from a coherent state. Relative phases between Fock basis components in the final state of STIRAP are determined by the phonon-number parity of the initial state. Furthermore, the system is numerically studied to determine the effects of dissipation, and it is concluded that high-fidelity entanglement can be achieved via fractional STIRAP using state-of-the-art cryogenic cooling and mechanical devices. Finally, an interferometric protocol using time-reversed fractional STIRAP is proposed to quantify entanglement between two mechanical modes.