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arXiv:1105.2336 · Physical Review A

Cavity quantum electro-optics. II. Input-output relations between traveling optical and microwave fields

Mankei Tsang

Published Oct 27, 2011• 113 citations
arXivHTMLPDF

Abstract

In a previous paper [Phys. Rev. A 81, 063837 (2010)], I proposed a quantum model of the cavity electro-optic modulator, which can coherently couple an optical cavity mode to a microwave resonator mode and enable quantum operations on the two modes, including laser cooling of the microwave resonator, electro-optic entanglement, and backaction-evading optical measurement of a microwave quadrature. In this sequel, I focus on the quantum input-output relations between traveling optical and microwave fields coupled to the cavity electro-optic modulator. With red-sideband optical pumping, the relations are shown to resemble those of a beam splitter for the traveling fields, so that in the ideal case of zero parasitic loss and critical coupling, microwave photons can be coherently up converted to ``flying'' optical photons with unit efficiency, and vice versa. With blue-sideband pumping, the modulator acts as a nondegenerate parametric amplifier, which can generate two-mode squeezing and hybrid entangled photon pairs at optical and microwave frequencies. These fundamental operations provide a potential bridge between circuit quantum electrodynamics and quantum optics.

DOI
10.1103/physreva.84.043845

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In a previous paper [Phys. Rev. A 81, 063837 (2010)], I proposed a quantum model of the cavity electro-optic modulator, which can coherently couple an optical cavity mode to a microwave resonator mode and enable quantum operations on the two modes, including laser cooling of the microwave resonator, electro-optic entanglement, and backaction-evading optical measurement of a microwave quadrature. In this sequel, I focus on the quantum input-output relations between traveling optical and microwave fields coupled to the cavity electro-optic modulator. With red-sideband optical pumping, the relations are shown to resemble those of a beam splitter for the traveling fields, so that in the ideal case of zero parasitic loss and critical coupling, microwave photons can be coherently up converted to ``flying'' optical photons with unit efficiency, and vice versa. With blue-sideband pumping, the modulator acts as a nondegenerate parametric amplifier, which can generate two-mode squeezing and hybrid entangled photon pairs at optical and microwave frequencies. These fundamental operations provide a potential bridge between circuit quantum electrodynamics and quantum optics.
The quantum dynamics of the coupling between a cavity optical field and a resonator microwave field via the electro-optic effect is studied. This coupling has the same form as the optomechanical coupling via radiation pressure, so all previously considered optomechanical effects can in principle be observed in electro-optic systems as well. In particular, I point out the possibilities of laser cooling of the microwave mode, entanglement between the optical mode and the microwave mode via electro-optic parametric amplification, and back-action-evading optical measurements of a microwave quadrature.
Linking classical microwave electrical circuits to the optical telecommunication band is at the core of modern communication. Future quantum information networks will require coherent microwave-to-optical conversion to link electronic quantum processors and memories via low-loss optical telecommunication networks. Efficient conversion can be achieved with electro-optical modulators operating at the single microwave photon level. In the standard electro-optic modulation scheme this is impossible because both, up- and downconverted, sidebands are necessarily present. Here we demonstrate true single sideband up- or downconversion in a triply resonant whispering gallery mode resonator by explicitly addressing modes with asymmetric free spectral range. Compared to previous experiments, we show a three orders of magnitude improvement of the electro-optical conversion efficiency reaching 0.1% photon number conversion for a 10GHz microwave tone at 0.42mW of optical pump power. The presented scheme is fully compatible with existing superconducting 3D circuit quantum electrodynamics technology and can be used for non-classical state conversion and communication. Our conversion bandwidth is larger than 1MHz and not fundamentally limited.
Quantum correlations, particularly squeezing and entanglement, are essential in quantum technologies such as metrology, computation, and simulation, as well as in foundational studies. In quantum optics, these phenomena are often intertwined: two squeezed beams can be transformed into entangled beams by mixing them at a beam splitter, and vice versa. However, it is less common to encounter states where two beams are simultaneously squeezed individually while retaining global entanglement. These hybrid states evidently present potential possibilities for applications. In this work, we propose a compact single-cavity source based on a nondegenerate optical parametric oscillator operated below threshold, capable of generating such light—signal and idler beams that are quadrature-squeezed individually while maintaining global entanglement. This behavior arises from an additional linear coupling between the signal and idler, resembling a beam-splitter interaction. We discuss two physical implementations of this system: one based on intra-cavity electro-optic modulators and the other on optomechanical interactions. This unique combination of local and non-local quantum correlations opens the door to novel quantum communication and metrology protocols.
Efficient conversion between microwave and optical photons is important for the development of hybrid quantum platforms in which quantum information is processed by superconducting circuits and transmitted with optical photons. A promising approach is to use electro-optic modulation with a microwave cavity coupled to an optical cavity, where microwave photons are up-converted to optical photons through sum frequency generation, and optical photons are converted to microwave photons through difference frequency generation. However, the frequency matching conditions in such set-ups usually require the size of the device to be large enough so that the optical frequencies of the pump and signal photons are supported. Hong Tang and colleagues have now fabricated a hybrid superconducting–photonic device that overcomes this limitation by using an integrated planar geometry to coherently convert between microwave and optical photons. adapted under a Creative Commons license CC BY-NC 4.0 ; AAAS
Abstract We propose an efficient microwave-photonic modulator as a resource for stationary entangled microwave-optical fields and develop the theory for deterministic entanglement generation and quantum state transfer in multi-resonant electro-optic systems. The device is based on a single crystal whispering gallery mode resonator integrated into a 3D-microwave cavity. The specific design relies on a new combination of thin-film technology and conventional machining that is optimized for the lowest dissipation rates in the microwave, optical, and mechanical domains. We extract important device properties from finite-element simulations and predict continuous variable entanglement generation rates on the order of a Mebit/s for optical pump powers of only a few tens of microwatts. We compare the quantum state transfer fidelities of coherent, squeezed, and non-Gaussian cat states for both teleportation and direct conversion protocols under realistic conditions. Combining the unique capabilities of circuit quantum electrodynamics with the resilience of fiber optic communication could facilitate long-distance solid-state qubit networks, new methods for quantum signal synthesis, quantum key distribution, and quantum enhanced detection, as well as more power-efficient classical sensing and modulation.
A number of schemes for a quantum interface between light at different wavelengths have been demonstrated and very recently various solutions for interfacing optics and microwaves have been proposed. We describe here a reversible quantum interface between optical and microwave photons based on a micro-mechanical resonator in a superconducting circuit, simultaneously interacting with an optical and a microwave cavity. When the cavities are appropriately driven, the mechanical resonator mediates an effective parametric amplifier interaction, entangling an optical signal and a microwave idler. Such continuous variable (CV) entanglement can be then exploited to implement CV teleportation. The optical output is mixed with an optical `client' field in an unknown quantum state on a beam splitter at the transmitting site (Alice). The two outputs are then subject to homodyne detection and the classical measurement results communicated to the receiving site (Bob). Upon receipt of these results, Bob makes a conditional displacement of the microwave field, again using beam splitters and a coherent microwave source. The resulting state of the output microwave field is then prepared in the same quantum state as the optical input state. The process is entirely symmetric: the Alice and Bob roles can be exchanged and an unknown input microwave field can be teleported onto the optical output field at Alice, realising therefore a reversible quantum state transfer between fields at completely different wavelengths.