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Physical Review A

Time-delayed entanglement from coherently coupled nonlinear cavities

T. McRae, Warwick P. Bowen

Published Jul 9, 2009• 7 citations
Publisher

Abstract

The output fields of a pair of coherently coupled nonlinear optical cavities are found to exhibit strong optical entanglement. For sufficiently strong coupling time-delayed quantum correlations are observed providing a resource for quantum information protocols such as all-optical quantum memories. A straightforward experimental implementation applicable to whispering gallery mode resonators such as microtoroids is proposed.

DOI
10.1103/physreva.80.010303

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Rare-earth-ion doped crystals are an interesting system for quantum computing investigations due to their long optical and hyperfine coherence times. In particular, the ground-state coherence times can be longer than one second, which makes them perfect for long-term storage of quantum states. They also have the advantage of being a solid-state system. At present, many of the fundamental requirements for quantum computing have been demonstrated using rare-earth-ions; however, quantum state readout has yet to be achieved. The strong-coupling regime is of great importance in cavity quantum electrodynamics, as in this regime interactions between single atoms and single photons can be realized. Strong coupling thereby provides a method of enabling qubit-qubit interactions. It is desirable to achieve this regime with rare-earth-ion doped resonators, as it would enable on-demand readout of quantum states, a necessity for quantum computing, and provide the scalability required for implementation of quantum networks. This thesis describes the work that has gone into investigating the suitability of rare-earth-ion doped whispering-gallery mode resonators for quantum computing applications. A theoretical analysis of the strong-coupling regime is performed, followed by experiments investigating the properties of ions in resonators, and of new rare-earth-ion materials. A final set of experiments studies a new quantum memory protocol for use with rare-earth-ions. A theoretical investigation is undertaken to determine whether the strong-coupling regime will be attainable with rare-earth-ion doped whispering-gallery mode resonators. Emphasis is given to determining which rare-earth-ion materials will have the best properties when used as resonators. Specific applications of the strong-coupling regime are examined for this system; in particular, whether it will be possible to demonstrate the reversible transfer of quantum states, and detection of single dopants. Experiments are performed, measuring the properties of millimetre-sized Pr3+:Y2SiO5 resonators. Direct measurements of cavity quantum electrodynamics parameters are made using photon echoes, giving good agreement with theoretical predictions. Interactions between the atom and cavity are observed and a theoretical model is presented to describe these effects. Thus, a more realistic picture is obtained of the experimental requirements for achieving the strong-coupling regime. The properties of different rare-earth-ion doped materials are measured and analysed to determine their suitability for quantum computing applications. The spin Hamiltonian parameters of Pr3+:YAG are measured using Raman heterodyne spectroscopy, and then used to find the optical transitions with zero first-order Zeeman shift, as this should allow the coherence time to be extended to a point where this system is useful for resonator applications. Hyperfine transitions with zero first-order Zeeman shift are also calculated for Er3+:Y2SiO5, with the aim of enabling long-term storage in a telecommunication-wavelength memory. The thesis concludes with an experimental investigation into a new quantum memory technique that does not require spectral hole burning. The hybrid photon echo rephasing protocol uses strong optical pulses to perform rephasing, thus utilizing the advantageous properties of the two-pulse photon echo. Furthermore, the use of external broadening fields removes the usual problem of noise from amplified spontaneous emission. The properties of this memory are examined using a Pr3+:Y2SiO5 crystal.

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The output fields of a pair of coherently coupled nonlinear optical cavities are found to exhibit strong optical entanglement. For sufficiently strong coupling time-delayed quantum correlations are observed providing a resource for quantum information protocols such as all-optical quantum memories. A straightforward experimental implementation applicable to whispering gallery mode resonators such as microtoroids is proposed.
A model is presented of nth order nonlinear processes in whispering gallery mode resonators, with scattering coherently coupling degenerate counter propagating modes. It is shown that such systems generate strong squeezing and time-delayed entanglement. The model can be generally applied to any pair of nonlinear coherently coupled cavities and is of particular relevance to whispering gallery mode resonators. A feature of the entanglement is that, by tuning the coherent coupling rate the peak entanglement can be tuned to occur away from the carrier frequency. This has technological significance allowing low frequency noise sources around the carrier frequency to be avoided. All-optical time-delayed entanglement has many applications, such as an all-optical quantum memory.
The paper presents a theoretical model of non-classical state generation in a pair of identical coupled nonlinear cavities operating in the below threshold optical parametric oscillator regime. The introduction of nonlinearity enables arbitrarily strong entanglement to be generated. However, for strong coupling, the entanglement is quenched, and a new form of asynchronous entanglement exhibiting time-delayed quantum correlations becomes apparent. The asynchronous entanglement predicted here has many applications in quantum information science.
We propose a scheme for single-atom, quantum control of the direction of propagation of a coherent field incident, via a tapered fiber, upon a microtoroidal whispering-gallery-mode (WGM) resonator. The scheme involves overcoupling of the fiber taper to the resonator and strong coupling of an atom to the evanescent field of the WGM, i.e., an atom-field coupling that exceeds the total WGM linewidth. In contrast to previous, related schemes that operate in the bad-cavity regime, the proposed scheme can operate effectively with much stronger incident fields, while also preserving their coherent nature. It can also serve to prepare an entangled state of the atom and coherent optical pulses propagating in opposite directions along the fiber. We evaluate the fidelity of preparation of such a state taking into account absorption and atomic spontaneous emission and demonstrate that high fidelities should be possible with realistic parameters.
Rare-earth-ion doped crystals are an interesting system for quantum computing investigations due to their long optical and hyperfine coherence times. In particular, the ground-state coherence times can be longer than one second, which makes them perfect for long-term storage of quantum states. They also have the advantage of being a solid-state system. At present, many of the fundamental requirements for quantum computing have been demonstrated using rare-earth-ions; however, quantum state readout has yet to be achieved. The strong-coupling regime is of great importance in cavity quantum electrodynamics, as in this regime interactions between single atoms and single photons can be realized. Strong coupling thereby provides a method of enabling qubit-qubit interactions. It is desirable to achieve this regime with rare-earth-ion doped resonators, as it would enable on-demand readout of quantum states, a necessity for quantum computing, and provide the scalability required for implementation of quantum networks. This thesis describes the work that has gone into investigating the suitability of rare-earth-ion doped whispering-gallery mode resonators for quantum computing applications. A theoretical analysis of the strong-coupling regime is performed, followed by experiments investigating the properties of ions in resonators, and of new rare-earth-ion materials. A final set of experiments studies a new quantum memory protocol for use with rare-earth-ions. A theoretical investigation is undertaken to determine whether the strong-coupling regime will be attainable with rare-earth-ion doped whispering-gallery mode resonators. Emphasis is given to determining which rare-earth-ion materials will have the best properties when used as resonators. Specific applications of the strong-coupling regime are examined for this system; in particular, whether it will be possible to demonstrate the reversible transfer of quantum states, and detection of single dopants. Experiments are performed, measuring the properties of millimetre-sized Pr3+:Y2SiO5 resonators. Direct measurements of cavity quantum electrodynamics parameters are made using photon echoes, giving good agreement with theoretical predictions. Interactions between the atom and cavity are observed and a theoretical model is presented to describe these effects. Thus, a more realistic picture is obtained of the experimental requirements for achieving the strong-coupling regime. The properties of different rare-earth-ion doped materials are measured and analysed to determine their suitability for quantum computing applications. The spin Hamiltonian parameters of Pr3+:YAG are measured using Raman heterodyne spectroscopy, and then used to find the optical transitions with zero first-order Zeeman shift, as this should allow the coherence time to be extended to a point where this system is useful for resonator applications. Hyperfine transitions with zero first-order Zeeman shift are also calculated for Er3+:Y2SiO5, with the aim of enabling long-term storage in a telecommunication-wavelength memory. The thesis concludes with an experimental investigation into a new quantum memory technique that does not require spectral hole burning. The hybrid photon echo rephasing protocol uses strong optical pulses to perform rephasing, thus utilizing the advantageous properties of the two-pulse photon echo. Furthermore, the use of external broadening fields removes the usual problem of noise from amplified spontaneous emission. The properties of this memory are examined using a Pr3+:Y2SiO5 crystal.