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arXiv:1002.0127 · Physical Review A

Quantum state engineering, purification, and number-resolved photon detection with high-finesse optical cavities

Anne E. B. Nielsen, Christine A. Muschik, G. Giedke, K. G. H. Vollbrecht

Published Apr 26, 2010• 10 citations
arXivHTMLPDF

Abstract

We propose and analyze a multifunctional setup consisting of high-finesse optical cavities, beam splitters, and phase shifters. The basic scheme projects arbitrary photonic two-mode input states onto the subspace spanned by the product of Fock states $|n\ensuremath{\rangle}|n\ensuremath{\rangle}$ with $n=0,1,2,\dots{}.$ This protocol does not only provide the possibility to conditionally generate highly entangled photon number states as resource for quantum information protocols but also allows one to test and hence purify this type of quantum states in a communication scenario, which is of great practical importance. The scheme is especially attractive as a generalization to many modes allows for distribution and purification of entanglement in networks. In an alternative working mode, the setup allows for quantum nondemolition number resolved photodetection in the optical domain.

DOI
10.1103/physreva.81.043832

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We propose and analyze a multifunctional setup consisting of high-finesse optical cavities, beam splitters, and phase shifters. The basic scheme projects arbitrary photonic two-mode input states onto the subspace spanned by the product of Fock states ∣n\ensuremath⟩∣n\ensuremath⟩|n\ensuremath{\rangle}|n\ensuremath{\rangle}∣n\ensuremath⟩∣n\ensuremath⟩ with n=0,1,2,….n=0,1,2,\dots{}.n=0,1,2,…. This protocol does not only provide the possibility to conditionally generate highly entangled photon number states as resource for quantum information protocols but also allows one to test and hence purify this type of quantum states in a communication scenario, which is of great practical importance. The scheme is especially attractive as a generalization to many modes allows for distribution and purification of entanglement in networks. In an alternative working mode, the setup allows for quantum nondemolition number resolved photodetection in the optical domain.
Photon-number Fock states play important roles in quantum optics. However, the generation of the states are very difficult because of the lack of large effective nonlinearities. In this Rapid Communication, I show a scheme to produce the Fock state from an input coherent state by using only linear optics method and projection measurements. I analyze the case of five-photon number state generation from coherent states for a specific case of the scheme. It is possible to remove the vacuum state from the output state when one introduces quantum nondemolition measurement that can also be implemented with all linear optics setup.
We propose an entanglement purification scheme based on material qubits and ancillary coherent multiphoton states. We consider a typical QED scenario where material qubits implemented by two-level atoms fly sequentially through a cavity and interact resonantly with a single mode of the radiation field. We explore the theoretical possibilities of realizing a high-fidelity two-qubit quantum operation necessary for the purification protocol with the help of a postselective balanced homodyne photodetection. We demonstrate that the obtained probabilistic quantum operation can be used as a bilateral operation in the proposed purification scheme. It is shown that the probabilistic nature of this quantum operation is counterbalanced in the last step of the scheme where qubits are not discarded after inadequate qubit measurements. As this protocol requires present-day experimental setups and generates high-fidelity entangled pairs with high repetition rates, it may offer interesting perspectives for applications in quantum information theory.
Photon catalysis is a technique by which a readily available Gaussian state of light prepared in one mode is incident upon a beam splitter with a discrete number of photons, q, prepared in another mode; the resulting two-mode state is then subjected to single-photon resolving detection for q photons on one of the output modes. By employing beam splitters of different transmissivities and reflectivities, the subsequent single-mode state is shown to possess nonclassical properties such as quadrature squeezing and sub-Poissonian statistics. We consider the case in which the input state is the most general of pure single-mode Gaussian states: a squeezed coherent state. Noting the Gaussianity of the initial state, we demonstrate non-Gaussianity of the photon-catalyzed state by analyzing the quadrature uncertainty product and explicitly illustrate it through the Wigner quasi-probability distribution. We extend this technique to the two-mode squeezed states, whereby we perform photon catalysis on one mode of a two-mode squeezed vacuum state. The resulting correlated two-mode state may have applications in fundamental tests of quantum mechanics, such as violations of Bell’s inequalities, as the detection loophole can be closed due to the non-Gaussianity of the photon-catalyzed state. We also generalize our method to include state projective measurements for l≠q photons.
In the framework of cavity QED, we propose a practical scheme to purify dynamically a bipartite entangled state using short chains of atoms coupled to high-finesse optical cavities. In contrast to conventional entanglement purification protocols, we avoid controlled-not gates, thus reducing complicated pulse sequences and superfluous qubit operations. Our interaction scheme works in a deterministic way and, together with entanglement distribution and swapping, opens a route toward efficient quantum repeaters for long-distance quantum communication.
A scheme is proposed for implementing a desired transformation of the unknown quantum state of a traveling optical multimode signal. The operator describing this transformation is built up as a polynomial in products of the mode operators. There is no limitation to unitary operators realized by the scheme, the implementation is conditional however, i.e., the desired operator can be realized only with a certain success probability which depends on the respective operator and the input state. While the scheme requires the preparation of single-photon and coherent states, it exclusively makes use of beam splitters and zero- and single-photon detections. The setup consists of a number of stations, each controlling one of the signal modes. The stations share an auxiliary entangled state which has been prepared beforehand. This state is then entangled with each of the signal modes and a measurement is performed of each of the auxiliary modes afterwards. In this way, the stations can be spatially separated from one another, similar to a multimode generalization of a quantum teleportation setup. Some examples of application such as the realization of cross-Kerr nonlinearities, multidirectional quantum teleportation (i.e., multimode mirrors), and the preparation of multimode Greenberger-Horne-Zeilinger- and Einstein-Podolsky-Rosen-like states are considered.
Protocols for probabilistic entanglement-assisted quantum teleportation and for entanglement swapping of material qubits are presented. They are based on a protocol for postselective Bell- state projection which is capable of projecting two material qubits onto a Bell state with the help of ancillary coherent multiphoton states and postselection by balanced homodyne photodetection. Provided this photonic postselection is successful, we explore the theoretical possibilities of realizing unit-fidelity quantum teleportation and entanglement swapping with 2525%25 success probability. This photon-assisted Bell projection is generated by coupling almost resonantly the two material qubits to single modes of the radiation field in two separate cavities in a Ramsey-type interaction sequence and by measuring the emerged field states in a balanced homodyne detection scenario. As these quantum protocols require basic tools of quantum state engineering of coherent multiphoton states and balanced homodyne photodetection, they may offer interesting perspectives in particular for current quantum optical applications in quantum information processing.