[Paper Review] Multimode quantum properties of a self-imaging OPO: squeezed vacuum and EPR beams generation

Luis A. Razo-López, Bénoît Chalopin+4 more|ArXiv.org|Dec 27, 2008

Quantum optics and atomic interactions3 citations

TL;DR

This paper demonstrates that a self-imaging optical parametric oscillator (OPO) generates highly multimode non-classical light, producing local squeezing and Einstein-Podolsky-Rosen (EPR) beams across transverse spatial modes. By leveraging the cavity's self-imaging property and solving for eigenmodes via Hermite-Gaussian decomposition, the system achieves up to 50 effective quantum modes with measurable squeezing, enabling applications in quantum imaging and multimode quantum communication.

ABSTRACT

We investigate the spatial quantum properties of the light emitted by a perfectly spatially degenerate optical parametric oscillator (self-imaging OPO). We show that this device produces local squeezing for areas bigger than a coherence are that depends on the crystal length and pump width. Furthermore, it generates local EPR beams in the far field. We show, calculating the eigenmodes of the system, that it is highly multimode for realistic experimental parameters.

Motivation & Objective

• To develop a source of highly multimode non-classical light with adjustable transverse shape for quantum information and imaging.
• To overcome limitations of conventional OPOs that filter transverse modes, by utilizing a self-imaging cavity that supports all transverse modes.
• To investigate the spatial quantum properties of light emitted by a self-imaging OPO, particularly local squeezing and EPR beam generation.
• To determine the effective number of quantum modes and their spatial structure under realistic experimental conditions.
• To establish a theoretical framework linking pump power, cavity parameters, and measurable squeezing in both near and far fields.

Proposed method

• Model the self-imaging OPO cavity using ABCD matrix formalism, ensuring the round-trip matrix equals identity for full transverse mode degeneracy.
• Derive the field operator decomposition in terms of transverse modes, using Hermite-Gaussian functions as a basis for the eigenmode analysis.
• Formulate the quantum Langevin equations for the intracavity field, incorporating gain, loss, and input noise via the coupling mirror transmission.
• Solve for the squeezing spectra using the input-output relations and quadrature operators, deriving the variance expressions in terms of eigenvalues of the interaction matrix $K_{int}$.
• Compute the eigenmodes of the system by diagonalizing $K_{int}$, showing they closely resemble Hermite-Gaussian modes with waist determined by pump width.
• Use the eigenmode decomposition to calculate measurable squeezing in arbitrary detector pixels via matrix inversion and noise propagation.

Experimental results

Research questions

• RQ1 Can a self-imaging OPO generate local squeezing across spatially extended areas larger than the coherence area?
• RQ2 Does the self-imaging OPO produce entangled EPR beams in the far field, and how does this depend on pump power and cavity parameters?
• RQ3 What is the effective number of independent quantum modes in the system, and how does it scale with crystal length and pump beam width?
• RQ4 How do the eigenmodes of the system relate to Hermite-Gaussian modes, and what is their spatial structure and squeezing profile?
• RQ5 Can the system support multimode quantum states suitable for quantum imaging and continuous-variable quantum communication?

Key findings

• The self-imaging OPO produces local squeezing over areas larger than the coherence area, which scales inversely with crystal length and pump beam width.
• The system generates local EPR beams in the far field, confirming its potential for quantum imaging and superresolution techniques.
• The eigenmodes of the system are well approximated by Hermite-Gaussian functions, with the fundamental mode corresponding to the highest gain and largest squeezing.
• For a 1 cm crystal and 300 µm pump waist at 1064 nm, the system supports approximately 50 effective quantum modes, as determined by the cooperativity $\kappa = 6.8$.
• Squeezing in individual eigenmodes decreases with mode number, with only modes having eigenvalues above ~10% of the maximum eigenvalue showing significant non-classicality.
• The measured squeezing in a detector of arbitrary shape is accurately predicted by both analytical models and numerical simulations using the eigenmode decomposition.