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arXiv:1210.2384 · Journal of Physics B Atomic Molecular and Optical Physics

Quantum circuits for amplification of Kerr nonlinearity via quadrature squeezing

Monika Bartkowiak, Lian-Ao Wu, Adam Miranowicz

Published Jul 4, 2014• 35 citations
arXivHTMLPDF

Abstract

Phase shifts induced by the Kerr effect are usually very small at the single-photon level. We propose two circuits for enhancing the cross-Kerr phase shift by applying one- and two-mode quadrature squeezing operators. Our results are based on the vector coherent state theory and can be implemented by physical operations satisfying the commutation relations for generators of the generalized special unitary group, SU(1,1). While the proposed methods could be useful for the realization of quantum optical entangling gates based on Kerr nonlinear media at the single-photon level, they also indicate a general alternative approach to enhance higher-order nonlinearities by applying lower-order nonlinear effects.

DOI
10.1088/0953-4075/47/14/145501

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Phase shifts induced by the Kerr effect are usually very small at the single-photon level. We propose two circuits for enhancing the cross-Kerr phase shift by applying one- and two-mode quadrature squeezing operators. Our results are based on the vector coherent state theory and can be implemented by physical operations satisfying the commutation relations for generators of the generalized special unitary group, SU(1,1). While the proposed methods could be useful for the realization of quantum optical entangling gates based on Kerr nonlinear media at the single-photon level, they also indicate a general alternative approach to enhance higher-order nonlinearities by applying lower-order nonlinear effects.
We develop squeezing protocols to enhance cross-Kerr interactions. We show that through alternating between squeezing along different quadratures of a single photonic mode, the cross-Kerr interaction strength can be generically amplified. As an application of the squeezing protocols, we discuss speeding up the deterministic implementation of controlled phase gates in photonic quantum computing architectures. We develop bounds that characterize how fast and strong single-mode squeezing has to be applied to achieve a desired gate error and show that the protocols can overcome photon losses. Finally, we discuss experimental realizations of the squeezing strategies in optical fibers and nanophotonic waveguides.
In quantum optics, squeezing corresponds to the process in which fluctuations of a quadrature operator are reduced below the shot noise limit. In turn, nonlinear squeezing can be defined as reduction of fluctuations related to nonlinear combination of quadrature operators. Quantum states with nonlinear squeezing are a necessary resource for deterministic implementation of high-order quadrature phase gates that are, in turn, sufficient for advanced quantum information processing. We demonstrate that this class of states can be deterministically prepared by employing a single self-Kerr gate accompanied by suitable Gaussian processing. The required Kerr coupling depends on the energy of the initial system and can be made arbitrarily small. We also employ numerical simulations to analyze the effects of imperfections and to show to which extent can they be neglected.
We develop squeezing protocols to enhance cross-Kerr interactions. We show that through alternating between squeezing along different quadratures of a single photonic mode, the cross-Kerr interaction strength can be generically amplified. As an application of the squeezing protocols, we discuss speeding up the deterministic implementation of controlled phase gates in photonic quantum computing architectures. We develop bounds that characterize how fast and strong single-mode squeezing has to be applied to achieve a desired gate error and show that the protocols can overcome photon losses. Finally, we discuss experimental realizations of the squeezing strategies in optical fibers and nanophotonic waveguides.
By employing displacement operations, single-photon subtractions, and weak cross-Kerr nonlinearity, we propose an alternative way of implementing several universal quantum logical gates for all-optical hybrid qubits encoded in both single-photon polarization state and coherent state. Since these schemes can be straightforwardly implemented only using local operations without teleportation procedure, therefore, less physical resources and simpler operations are required than the existing schemes. With the help of displacement operations, a large phase shift of the coherent state can be obtained via currently available tiny cross-Kerr nonlinearity. Thus, all of these schemes are nearly deterministic and feasible under current technology conditions, which makes them suitable for large-scale quantum computing.
Weak cross-Kerr nonlinearities between single photons and coherent states are the basis for many applications in quantum-information processing. These nonlinearities have so far mainly been discussed in terms of highly idealized single-mode models. We develop a general theory of the interaction between continuous-mode photonic pulses and apply it to the case of a single photon interacting with a coherent state. We quantitatively study the validity of the usual single-mode approximation using the concepts of fidelity and conditional phase. We show that high fidelities, nonzero conditional phases, and high photon numbers are compatible, under conditions where the pulses fully pass through each other and where unwanted transverse-mode effects are suppressed.
The cross-Kerr nonlinearity (XKNL) effect can induce efficient photon interactions in principle with which photonic multiqubit gates can be performed using far fewer physical resources than linear optical schemes. Unfortunately, it is extremely challenging to generate giant cross-Kerr nonlinearities. In recent years much effort has been made to perform multiqubit gates via weak XKNLs. However, the required nonlinearity strengths are still difficult to achieve in an experiment. We here propose an XKNL-based scheme for realizing a two-photon polarization-parity gate, a universal two-qubit gate, in which the required strength of the nonlinearity could be orders of magnitude weaker than those required for previous schemes. The scheme utilizes a ring cavity fed by a coherent state as a quantum information bus which interacts with a path mode of the two polarized photons (qubits). The XKNL effect makes the bus pick up a phase shift dependent on the photon number of the path mode. Even when the potential phase shifts are very small they can be effectively measured using photon-number resolving detectors, which accounts for the fact that our scheme can work in the regime of tiny XKNL. The measurement outcome reveals the parity (even parity or odd parity) of the two polarization qubits.