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Annual Meeting Optical Society of America

Ultrasqueezed light via multifrequency pumping

Bonny L. Schumaker

Published Jan 1, 1986• 1 citation
Publisher

Abstract

The fundamental and simplest kind of squeezing (broadband squeezing) is produced by pumping a nonlinear medium at a single frequency. The observables squeezed are the electric-field quadrature phases defined relative to the pump frequency. Their measurement requires homodyning against an optical-frequency (the pump frequency) local oscillator. When the medium is pumped at several different frequencies (equally spaced), different kinds of observables exhibit squeezing. Their measurement requires further homodyning, against a radio-frequency (the pump frequency spacing) local oscillator, and, for four or more pump frequencies, against subsequent lower-frequency local oscillators. For a given total pump power, it is possible to achieve greater squeezing by distributing the pump power over several (at least three) different pump frequencies than by pumping at a single frequency. The drawback is that a more sophisticated detection scheme is required (i.e., further homodyning) to measure the maximum squeezing (less squeezing is produced in more easily measured observables, such as the electric-field quadrature phases). The required further homodyning at rf and lower frequencies is straightforward to accomplish, however, and the advantages of using lower pump powers at each optical frequency can be substantial, especially in mediums such as optical fibers, where large pump powers bring with them substantial added noise sources.

DOI
10.1364/oam.1986.tua8

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What's so ultra about ultrasqueezed light?

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At a previous OSA conference the author introduced the phenomenon of ultrasqueezed light, produced by three-wave and four-wave mixing in nonlinear media pumped at multiple frequencies spaced so as to produce appropriate phase-matching. Here quantitative results are given of the advantages offered by ultrasqueezing in terms of the degree of squeezing obtainable for a given total amount of input pump power. Phase-matching requirements and detection techniques are described, and resulting implications for the usefulness (enhanced squeezing vs ease of production and detection) are indicated. The results differ appreciably for three-wave and four-wave mixing. Several different experimental schemes for producing ultrasqueezed light are described using three-wave and four-wave mixing. Only one of these, four-wave mixing with two pump frequencies in an optical fiber, has been attempted experimentally; its success has been described at a previous OSA conference and is reviewed only briefly. Comparison is made between ultrasqueezed light and pulsed squeezed light, which can be viewed as a special limit of ultrasqueezing with many pump frequencies.

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Transmission and accurate detection of squeezed states of light will play a central role in the future quantum internet, where quantum cryptography, communication and computation will coexist in an organic system. Their coherent detection has recently proven to be crucial for photonics-based quantum computing [1] , and to provide improvements in continuous variables quantum key distribution [2] [6] and quantum sensing [3] . Often when measuring a quantum state through coherent detection, the local oscillator field is transmitted along with the signal; however, in realistic long-distance optical fiber transmissions, where the needed local oscillator optical power increases exponentially with the distance, the system’s performance deteriorates due to nonlinear Brillouin scattering, and wavelength multiplexing schemes may be needed to avoid the issue. Moreover, transmitting a local oscillator opens security loopholes in quantum key distribution systems, where an eavesdropper can defy the security assessment from the trusted parties by gaining control over the local oscillator [4] . It is therefore very important to design coherent detection schemes that make use of independent local oscillators. We demonstrate the transmission single-mode squeezed light at 1550 nm wavelength through single-mode optical fibers (10 m and 10 km lengths) and its homodyne detection, using an independent local oscillator and a real-time phase-control system. Fig. 1a depicts the implemented physical setup: 1550 nm squeezed light is generated through spontaneous parametric downconversion [5] , couples into a single-mode optical fiber and propagates towards the homodyne detector for quadrature measurement. Real-time phase control consists in detecting the interference between a 40 MHz single-sideband pilot mode -phase-locked to the downconverted pump- and the local oscillator, estimating their instantaneous phase difference and implementing a fast and broad FPGA-based phase control on the local oscillator. As shown in Fig. 1b and 1c, with the presented scheme it was possible to steadily measure up to 3.6 dB of squeezing after a 10 m optical fiber transmission, and up to 1.5 dB of squeezing after a 10 km fiber transmission, with similar performance in terms of phase error and control stability. The presented system is simple, robust and cost-effective, and it will represent a standard class of techniques to detect not only squeezed states of light, but any arbitrary quantum state of light, including Schrödinger cat states, highly useful in quantum computation and error correction.

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The degree of squeezing generated by parametric downconversion or four-wave mixing can be limited by the ratio of the nonlinear coupling to the linear losses in many practical systems. This ratio can be enhanced by increasing the pump power used for the nonlinear coupling in many solid nonlinear systems where the linear losses are not directly related to the nonlinear squeezing process. Pulsed pump sources are attractive for optimizing the nonlinear coupling-to-loss ratio. We have shown1 that homodyne detection can be used to detect the pulsed squeezing generated by a mode-locked pulse train from the pump laser. A portion of the pump beam is used as the local oscillator which stroboscopically samples portions of the squeezed light pulse train. The amount of squeezing which can be measured as a function of the relative durations of the pump and local oscillator pulses is shown. Progress of recent experiments using both four-wave mixing and parametric downconversion is described.

Annual Meeting Optical Society of America•Jan 1, 1987•0 citations
The fundamental and simplest kind of squeezing (broadband squeezing) is produced by pumping a nonlinear medium at a single frequency. The observables squeezed are the electric-field quadrature phases defined relative to the pump frequency. Their measurement requires homodyning against an optical-frequency (the pump frequency) local oscillator. When the medium is pumped at several different frequencies (equally spaced), different kinds of observables exhibit squeezing. Their measurement requires further homodyning, against a radio-frequency (the pump frequency spacing) local oscillator, and, for four or more pump frequencies, against subsequent lower-frequency local oscillators. For a given total pump power, it is possible to achieve greater squeezing by distributing the pump power over several (at least three) different pump frequencies than by pumping at a single frequency. The drawback is that a more sophisticated detection scheme is required (i.e., further homodyning) to measure the maximum squeezing (less squeezing is produced in more easily measured observables, such as the electric-field quadrature phases). The required further homodyning at rf and lower frequencies is straightforward to accomplish, however, and the advantages of using lower pump powers at each optical frequency can be substantial, especially in mediums such as optical fibers, where large pump powers bring with them substantial added noise sources.
At a previous OSA conference the author introduced the phenomenon of ultrasqueezed light, produced by three-wave and four-wave mixing in nonlinear media pumped at multiple frequencies spaced so as to produce appropriate phase-matching. Here quantitative results are given of the advantages offered by ultrasqueezing in terms of the degree of squeezing obtainable for a given total amount of input pump power. Phase-matching requirements and detection techniques are described, and resulting implications for the usefulness (enhanced squeezing vs ease of production and detection) are indicated. The results differ appreciably for three-wave and four-wave mixing. Several different experimental schemes for producing ultrasqueezed light are described using three-wave and four-wave mixing. Only one of these, four-wave mixing with two pump frequencies in an optical fiber, has been attempted experimentally; its success has been described at a previous OSA conference and is reviewed only briefly. Comparison is made between ultrasqueezed light and pulsed squeezed light, which can be viewed as a special limit of ultrasqueezing with many pump frequencies.
The four-wave-mixing interactions produced by pumping at two well-separated frequencies can couple four different radiation modes to generate a new kind of squeezed state of light. A dual-frequency homodyne detection scheme is described and is used to observe this type of nonclassical correlation. Initial experimental results in an optical fiber show a noise level 20% below the vacuum noise level for the output of the dual-frequency detector, even though the noise at each individual detector remains above the vacuum level.
Transmission and accurate detection of squeezed states of light will play a central role in the future quantum internet, where quantum cryptography, communication and computation will coexist in an organic system. Their coherent detection has recently proven to be crucial for photonics-based quantum computing [1] , and to provide improvements in continuous variables quantum key distribution [2] [6] and quantum sensing [3] . Often when measuring a quantum state through coherent detection, the local oscillator field is transmitted along with the signal; however, in realistic long-distance optical fiber transmissions, where the needed local oscillator optical power increases exponentially with the distance, the system’s performance deteriorates due to nonlinear Brillouin scattering, and wavelength multiplexing schemes may be needed to avoid the issue. Moreover, transmitting a local oscillator opens security loopholes in quantum key distribution systems, where an eavesdropper can defy the security assessment from the trusted parties by gaining control over the local oscillator [4] . It is therefore very important to design coherent detection schemes that make use of independent local oscillators. We demonstrate the transmission single-mode squeezed light at 1550 nm wavelength through single-mode optical fibers (10 m and 10 km lengths) and its homodyne detection, using an independent local oscillator and a real-time phase-control system. Fig. 1a depicts the implemented physical setup: 1550 nm squeezed light is generated through spontaneous parametric downconversion [5] , couples into a single-mode optical fiber and propagates towards the homodyne detector for quadrature measurement. Real-time phase control consists in detecting the interference between a 40 MHz single-sideband pilot mode -phase-locked to the downconverted pump- and the local oscillator, estimating their instantaneous phase difference and implementing a fast and broad FPGA-based phase control on the local oscillator. As shown in Fig. 1b and 1c, with the presented scheme it was possible to steadily measure up to 3.6 dB of squeezing after a 10 m optical fiber transmission, and up to 1.5 dB of squeezing after a 10 km fiber transmission, with similar performance in terms of phase error and control stability. The presented system is simple, robust and cost-effective, and it will represent a standard class of techniques to detect not only squeezed states of light, but any arbitrary quantum state of light, including Schrödinger cat states, highly useful in quantum computation and error correction.
A photodetector's electronic bandwidth is the frequency range over which beats between different frequencies in the input can be observed in the output. The output of a balanced homodyne detector, the prototypical device for detecting squeezed light, consists of beats between a signal to be measured and a local oscillator. Beats between the signal and quantum local-oscillator fluctuations lead to noise that degrades the observed squeezing. Through wide-band calculations, we show that this noise contains contributions from the entire signal bandwidth, even when this bandwidth is orders of magnitude larger than the detector's electronic bandwidth. This allows us to place an upper limit on the total power that can enter the detector's signal port (both signal and extraneous light) within the detector's optical bandwidth in order for a given level of squeezing to be observable.
Homodyne measurement is a corner-stone of quantum optics. It measures the fundamental variables of quantum electrodynamics - the quadratures of light, which represent the cosine-wave and sine-wave components of an optical field and constitute the quantum optical analog of position and momentum. Yet, standard homodyne, which is used to measure the quadrature information, suffers from a severe bandwidth limitation: While the bandwidth of optical states can easily span many THz, standard homodyne detection is inherently limited to the electrically accessible, MHz to GHz range, leaving a dramatic gap between the relevant optical phenomena and the measurement capability. We demonstrate a fully parallel optical homodyne measurement across an arbitrary optical bandwidth, effectively lifting this bandwidth limitation completely. Using optical parametric amplification, which amplifies one quadrature while attenuating the other, we measure two-mode quadrature squeezing of 1.7dB below the vacuum level simultaneously across a bandwidth of 55THz, using just one local-oscillator - the pump. As opposed to standard homodyne, our measurement is highly robust to detection inefficiency, and was obtained with >50%>50\%>50% loss in the detection channel. This broadband parametric homodyne measurement opens a wide window for parallel processing of quantum information.
The degree of squeezing generated by parametric downconversion or four-wave mixing can be limited by the ratio of the nonlinear coupling to the linear losses in many practical systems. This ratio can be enhanced by increasing the pump power used for the nonlinear coupling in many solid nonlinear systems where the linear losses are not directly related to the nonlinear squeezing process. Pulsed pump sources are attractive for optimizing the nonlinear coupling-to-loss ratio. We have shown1 that homodyne detection can be used to detect the pulsed squeezing generated by a mode-locked pulse train from the pump laser. A portion of the pump beam is used as the local oscillator which stroboscopically samples portions of the squeezed light pulse train. The amount of squeezing which can be measured as a function of the relative durations of the pump and local oscillator pulses is shown. Progress of recent experiments using both four-wave mixing and parametric downconversion is described.