Multimode Squeezing Properties of a Confocal Opo: Beyond the Thin Crystal Approximation

Up to now, transverse quantum effects (usually labelled as "quantum imaging" effects) which are generated by nonlinear devices inserted in resonant optical cavities have been calculated using the "thin crystal approximation", i.e. taking into account the effect of diffraction only inside the empty part of the cavity, and neglecting its effect in the nonlinear propagation inside the nonlinear crystal. We introduce in the present paper a theoretical method which is not restricted by this approximation. It allows us in particular to treat configurations closer to the actual experimental ones, where the crystal length is comparable to the Rayleigh length of the cavity mode. We use this method in the case of the confocal OPO, where the thin crystal approximation predicts perfect squeezing on any area of the transverse plane, whatever its size and shape. We find that there exists in this case a "coherence length" which gives the minimum size of a detector on which perfect squeezing can be observed, and which gives therefore a limit to the improvement of optical resolution that can be obtained using such devices.Comment: soumis le 04.03.2005 a PR

Observation of squeezed light from one atom excited with two photons

Single quantum emitters like atoms are well-known as non-classical light sources which can produce photons one by one at given times, with reduced intensity noise. However, the light field emitted by a single atom can exhibit much richer dynamics. A prominent example is the predicted ability for a single atom to produce quadrature-squeezed light, with sub-shot-noise amplitude or phase fluctuations. It has long been foreseen, though, that such squeezing would be "at least an order of magnitude more difficult" to observe than the emission of single photons. Squeezed beams have been generated using macroscopic and mesoscopic media down to a few tens of atoms, but despite experimental efforts, single-atom squeezing has so far escaped observation. Here we generate squeezed light with a single atom in a high-finesse optical resonator. The strong coupling of the atom to the cavity field induces a genuine quantum mechanical nonlinearity, several orders of magnitude larger than for usual macroscopic media. This produces observable quadrature squeezing with an excitation beam containing on average only two photons per system lifetime. In sharp contrast to the emission of single photons, the squeezed light stems from the quantum coherence of photon pairs emitted from the system. The ability of a single atom to induce strong coherent interactions between propagating photons opens up new perspectives for photonic quantum logic with single emittersComment: Main paper (4 pages, 3 figures) + Supplementary information (5 pages, 2 figures). Revised versio

Squeezed Light and Entangled Images from Four-Wave-Mixing in Hot Rubidium Vapor

Entangled multi-spatial-mode fields have interesting applications in quantum information, such as parallel quantum information protocols, quantum computing, and quantum imaging. We study the use of a nondegenerate four-wave mixing process in rubidium vapor at 795 nm to demonstrate generation of quantum-entangled images. Owing to the lack of an optical resonator cavity, the four-wave mixing scheme generates inherently multi-spatial-mode output fields. We have verified the presence of entanglement between the multi-mode beams by analyzing the amplitude difference and the phase sum noise using a dual homodyne detection scheme, measuring more than 4 dB of squeezing in both cases. This paper will discuss the quantum properties of amplifiers based on four-wave-mixing, along with the multi mode properties of such devices.Comment: 11 pages, 8 figures. SPIE Optics and Photonics 2008 proceeding (San Diego, CA

Quantum interference in two-photon excitation with squeezed and coherent fields

Two-photon excitation of a three-level atom in a ladder configuration (1-->2-->3) by simultaneous illumination with fields in squeezed vacuum and coherent states results in quantum interference for the excitation process. The particular configuration considered here is one for which the signal and idler output fields of a subthreshold nondegenerate optical parametric oscillator are in resonance with the two-stepwise dipole atomic transitions (1-->2,2-->3), while a "reference oscillator" field is in two-photon resonance with the quadrupole transition (1-->3). In an extension of the work of Ficek and Drummond [Phys. Rev. A 43, 6247 (1991)], a theoretical formulation based on the full quantum master equation for the problem is presented. The combined effects of quantum interference and the nonclassical character of the squeezed state are investigated, and offer the potential for a new detection strategy for quantum fluctuations of the electromagnetic field with ultrahigh frequencies (10's-100's THz). Based on the theory developed, we analyze quantum interference in excitation in several special cases relevant to experimental realizations, including the effects of a small focusing angle of the squeezing onto the atoms, and unusual population inversions. Special emphasis is given to identifying intrinsically quantum optical field effects versus classical field effects. Procedures that could distinguish between the two (i.e., classical and nonclassical) are suggested

Frequency noise cancellation in optomechanical systems for ponderomotive squeezing

Ponderomotive squeezing of the output light of an optical cavity has been recently observed in the MHz range in two different cavity optomechanical devices. Quadrature squeezing becomes particularly useful at lower spectral frequencies, for example in gravitational wave interferometers, despite being more sensitive to excess phase and frequency noise. Here we show a phase/frequency noise cancellation mechanism due to destructive interference which can facilitate the production of ponderomotive squeezing in the kHz range and we demonstrate it experimentally in an optomechanical system formed by a Fabry-P\'{e}rot cavity with a micro-mechanical mirror.Comment: 11 pages, 9 figures. Physical explanation expanded. Modified figure

Theory of Two-Photon Interactions with Broadband Down-Converted Light and Entangled Photons

When two-photon interactions are induced by down-converted light with a bandwidth that exceeds the pump bandwidth, they can obtain a behavior that is pulse-like temporally, yet spectrally narrow. At low photon fluxes this behavior reflects the time and energy entanglement between the down-converted photons. However, two-photon interactions such as two-photon absorption (TPA) and sum-frequency generation (SFG) can exhibit such a behavior even at high power levels, as long as the final state (i.e. the atomic level in TPA, or the generated light in SFG) is narrowband enough. This behavior does not depend on the squeezing properties of the light, is insensitive to linear losses, and has potential applications. In this paper we describe analytically this behavior for travelling-wave down-conversion with continuous or pulsed pumping, both for high- and low-power regimes. For this we derive a quantum-mechanical expression for the down-converted amplitude generated by an arbitrary pump, and formulate operators that represent various two-photon interactions induced by broadband light. This model is in excellent agreement with experimental results of TPA and SFG with high power down-converted light and with entangled photons [Dayan et al., Phys. Rev. Lett. 93, 023005 (2004), Dayan et al., Phys. Rev. Lett. 94, 043602, (2005), Pe'er et al., Phys. Rev. Lett. 94, 073601 (2005)].Comment: 23 pages, 4 figures, submitted to Phys. Rev.