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Physical Review A

Feedback-enhanced squeezing in second-harmonic generation

Howard M. Wiseman, Matthew S. Taubman, Hans‐A. Bachor

Published Apr 1, 1995• 30 citations

Abstract

Second-harmonic generation, in a cavity resonant only at the fundamental, produces amplitude squeezing in both the fundamental and the second harmonic, with optimal squeezing of -1/3 and -8/9, respectively, at low frequency. It also produces nonclassical correlations between the two output beams. We show that these correlations can be used to enhance the squeezing in either beam by constructing a feedback loop. By using the second-harmonic photocurrent to control the amplitude of the pump, the optimal fundamental squeezing is enhanced by 50% to -1/2. The limit of -8/9 for the seocnd harmonic (for infinite nonlinearity strength) cannot be improved by feeding back the fundamental. However, for any fixed finite nonlinearity, such feedback can produce significant enhancement, with a maximum of 50%. Even with the losses characteristic of a practical experiment included, the enchancement offered by the feedback is still significant, being greater than 20% in either mode.

DOI: 10.1103/physreva.51.3227

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Second-harmonic generation, in a cavity resonant only at the fundamental, produces amplitude squeezing in both the fundamental and the second harmonic, with optimal squeezing of -1/3 and -8/9, respectively, at low frequency. It also produces nonclassical correlations between the two output beams. We show that these correlations can be used to enhance the squeezing in either beam by constructing a feedback loop. By using the second-harmonic photocurrent to control the amplitude of the pump, the optimal fundamental squeezing is enhanced by 50% to -1/2. The limit of -8/9 for the seocnd harmonic (for infinite nonlinearity strength) cannot be improved by feeding back the fundamental. However, for any fixed finite nonlinearity, such feedback can produce significant enhancement, with a maximum of 50%. Even with the losses characteristic of a practical experiment included, the enchancement offered by the feedback is still significant, being greater than 20% in either mode.

A new method of amplitude squeezing a second-harmonic signal with negative feedback will be discussed. Negative feedback is known to produce amplitude squeezing in diode lasers.1 Previous studies of second-harmonic squeezing that did not include negative feedback predicted no squeezing to the sixth order in the low-conversion-efficiency limit2 and 3 dB squeezing in the limit of 100- conversion efficiency.3 By employing negative feedback, substantial squeezing is possible in the low-conversion-efficiency regime. Amplitude noise reductions in excess of 10 dB are possible. This approach does not require a resonant cavity to enhance amplitude squeezing. The squeezing dependence on key system parameters, such as second- harmonic photon number, will be discussed.

We discuss quantum-fluctuation characteristics of a second-harmonic generation system that uses an optical resonator to confine only the fundamental field. It was predicted that the available amount of squeezing is limited to 1.76 dB for the fundamental output and 9.54 dB for the second-harmonic output, respectively, irrespective of system parameters. However, these predictions are based on low-order perturbation theory and are unavailable if the nonlinear coupling between the fundamental and the second harmonic becomes large. We consider the spatial evolution of the fields and reveal that the maximum amount of squeezing depends on the cavity loss: Even an arbitrary amount of squeezing is possible for both the fundamental output and the second-harmonic output. We also consider the possibility of parametric oscillation of empty cavity modes pumped by the generated second harmonic and derive the following prediction: In a system that uses a type I phase-matched crystal, the oscillation of the side mode hardly occurs because of sum-frequency generation with the fundamental and scarcely imposes any limitations on squeezing. On the other hand, a system with a type II phase-matched crystal suffers from the oscillation of the polarization mode orthogonal to that of the fundamental input, and squeezing of the second-harmonic output is limited to 3 dB.

We analyze the squeezing characteristics of a singly resonant second-harmonic-generation system, in which only the fundamental light is confined in a plain cavity resonator, with consideration for fundamental depletion in a nonlinear crystal. The system was analyzed under the mean-field approximation, which neglects the variation of the field in the crystal, and as much as 9.5 dB of squeezing was predicted in the second-harmonic output. On the basis of the self-consistent method, we analyze the system, which is driven by such an intense fundamental input that the mean-field approximation is not valid, and predict that an arbitrary amount of squeezing will be available in this regime.

We present a technique for generation of tripartite quantum-correlated amplitude-squeezed light beams, using frequency doubling in a singly resonant cavity with two output ports. The two-output second-harmonic (SH) beams are both nonlinearly coupled to the common fundamental beam even though they have no direct interaction. The nonlinear coupling produces noise reduction of amplitude for each beam and quantum correlations among three beams. In our first experiment, we measured amplitude squeezing of 0.5, 0.8, and 0.6 dB for the fundamental beam and two output SH beams, respectively. Meanwhile, quantum correlation of 0.6 dB between the two amplitude-squeezed SH beams and quantum anticorrelation of 0.6 and 0.8 dB between the squeezed fundamental beam and each of the SH beams were observed around the range of optimum conversion efficiency. This opens an alternate way to produce tripartite-quantum-correlated systems.