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Frontiers in Optics

Parametric amplification of a quantum pulse

Offek Tziperman, Victor Rueskov Christiansen, Klaus Mølmer

Published Jan 1, 2023• 0 citations
Publisher

Abstract

We present a theory for the transformation of quantum wave packets by parametric amplifiers. We find that input wave packets couple to only two output modes and can be amplified without significant addition of noise.
DOI
10.1364/fio.2023.jtu5a.82

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A single quantum pulse undergoing parametric amplification feeds into at most two pulses in the output. In this work, we present an efficient, analytical method for finding the quantum state of these output modes. Our method applies the amplification to the vacuum rather than to the input state, and subsequently applies a transformed version of the operator that creates the input state from vacuum. Given the input and output pulse mode functions, the method is analytical, and therefore computationally very efficient, and it can be readily generalized to multiple non-vacuum input modes. We exemplify the method by computing the output quantum states resulting from the input of a coherent, a Schrödinger cat, and a single photon input quantum state. We further employ the method to obtain the quantum state in one of the two output modes heralded upon detection of vacuum in the other, least populated, mode.
Creating and manipulating quantum states of light requires nonlinear interactions. We present here a multimode theory for the transformation of an arbitrary quantum pulse by Hamiltonians that are quadratic in field creation and annihilation operators. We show, in particular, that any input quantum pulse will feed only one or two distinct output modes. Our result readily provides both the output modes and the quantum states after transformation of arbitrary input wave packets. While being central for applications in quantum information processing with traveling bosonic modes, e.g., in quantum networks, our theoretical method and its results are not anticipated by the conventional Bogoliubov diagonalization of the problem in many input and output eigenmodes.
Quantum fluctuations in an optical amplifier are of fundamental as well as technological significance and lead to basic limitations on noise performance. It is well-known that the signal-to-noise ratio (SNR) of an injected signal is degraded in the amplification process due to added noise from thermal or (at best) vacuum fluctuations of the internal modes of the amplifier.[1] However, if the internal modes are coupled to a squeezed vacuum, the added noise in amplification can be reduced.[2] With this motivation, we have constructed a nondegenerate parametric amplifier whose idler mode is itself coupled to a squeezed vacuum, which is generated by a second parametric amplifier. Phase-sensitive noise amplification of a vacuum input to the signal mode is observed with the minimum amplified noise level 0.5dB below the usual phase-insensitive amplified noise level for the amplified signal of the same amplifier but with the idler mode coupled to a vacuum state. Prospects for improvement by increasing the squeezing that is coupled into the idler mode of the amplifier beyond the current level of 2dB as well as surprising results from our theoretical analysis which includes losses will be discussed.
Amplification of an entangled state is a matter of great significance in quantum communication. However, any parametric amplifier (PA) will introduce added noise into the system which unavoidably degrades the entanglement or even makes it disappear. Recently, it has been experimentally demonstrated that amplification of one half of a two-mode squeezed state is possible while preserving entanglement [Phys. Rev. Lett. 103, 010501 (2009)]. However, such entanglement cannot be maintained when the strength of the amplification is large. To solve this problem, we propose a correlation modulation scheme (CMS), which fully exploits the quantum correlation between the two output states from the PA process, to suppress the added noise from the parametric amplifications. For amplifying an entangled state using a PA, we demonstrate that the CMS not only better maintains but also always preserves the entanglement whatever the strength of the PA. Such a CMS may pave the way to low-noise amplification of an entangled state.