Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Summary

We describe the reliable generation of non-Gaussian states of traveling optical fields, including single-photon states and coherent state superpositions, using a conditional preparation method operated on the non-classical light emitted by optical parametric oscillators. Type-I and type-II phase-matched oscillators are considered and common procedures, such as the required frequency filtering or the high-efficiency quantum state characterization by homodyning, are detailed.

Abstract

Engineering non-classical states of the electromagnetic field is a central quest for quantum optics^1,2. Beyond their fundamental significance, such states are indeed the resources for implementing various protocols, ranging from enhanced metrology to quantum communication and computing. A variety of devices can be used to generate non-classical states, such as single emitters, light-matter interfaces or non-linear systems³. We focus here on the use of a continuous-wave optical parametric oscillator^3,4. This system is based on a non-linear χ² crystal inserted inside an optical cavity and it is now well-known as a very efficient source of non-classical light, such as single-mode or two-mode squeezed vacuum depending on the crystal phase matching.
Squeezed vacuum is a Gaussian state as its quadrature distributions follow a Gaussian statistics. However, it has been shown that number of protocols require non-Gaussian states⁵. Generating directly such states is a difficult task and would require strong χ³ non-linearities. Another procedure, probabilistic but heralded, consists in using a measurement-induced non-linearity via a conditional preparation technique operated on Gaussian states. Here, we detail this generation protocol for two non-Gaussian states, the single-photon state and a superposition of coherent states, using two differently phase-matched parametric oscillators as primary resources. This technique enables achievement of a high fidelity with the targeted state and generation of the state in a well-controlled spatiotemporal mode.

Introduction

The ability to engineer the quantum state of traveling optical fields is a central requirement for quantum information science and technology¹, including quantum communication, computing and metrology. Here, we discuss the preparation and characterization of some specific quantum states using as a primary resource the light emitted by continuous-wave optical parametric oscillators^3,4 operated below threshold. Specifically, two systems will be considered – a type-II phase-matched OPO and a type-I OPO – enabling respectively the reliable generation of heralded single-photons and of optical coherent state superpositions (CSS), i.e. states o....

Protocol

1. Optical Parametric Oscillator

1. Build a 4 cm long semimonolithic linear cavity (for improved mechanical stability and reduced intracavity losses). The input mirror is directly coated on one face of the nonlinear crystal.
2. Choose an input coupler reflection of 95% for the pump at 532 nm and high-reflection for the signal and idler at 1,064 nm. Inversely, choose the output coupler to be highly reflective for the pump and of transmittance T=10% for the infrared. The free spectral range of the OPO is equal to Δω = 4.3 GHz and the bandwidth is around 60 MHz. Make the cavity triply resonant, i.e. for the pump and for the down-co....

Results

For the type-II OPO and the generation of high-fidelity single photon state:
The tomographic reconstruction of the heralded state is shown in Figure 2, where the diagonal elements of the reconstructed density matrix and the corresponding Wigner function are displayed. Without any loss corrections, the heralded state exhibits a single-photon component as high as 78%. By taking into account the overall detection losses (15%), the state reaches a fidelity of 91% with a single-photon state. The two-photo.......

Discussion

The conditional preparation technique presented here is always an interplay between the initial bipartite resource and the measurement performed by the heralding detector. These two components strongly influence the quantum properties of the generated state.

First, the purity of the prepared states strongly depends on the one of the initial resource, thus a ‘good’ OPO is required. What is a ‘good’ OPO? It is a device for which the escape efficiency η is close to un.......

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Pump laser	Innolight	Diabolo	Dual output, IR and 532 nm
KTP and PPKTP crystal	Raicol		Available from other vendors
Interferential filters	Barr associates
High efficiency photodiodes	Fermionics		Quantum efficiency above 97%
Oscilloscope	Lecroy	Wave runner 610 Zi	Used for data acquisition
Spectrum analyser	Agilent	N9000A	Available from other vendors
Faraday rotator	Qioptic	FR-1060-5SC	Available from other vendors
PZT	PI	P-016.00H	Available from other vendors
Superconducting single-photon detectors	Scontel	SSPD	low dark counts
Optical switch	Thorlabs	OSW12-980E	Available from other vendors