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Annual Meeting Optical Society of America

High-gain spatial distortion limits for squeezing and quantum measurement

Arthur La Porta, R. E. Slusher

Published Jan 1, 1990• 0 citations
Publisher

Abstract

The single-pass parametric downconver- sion amplifier is a simple optical arrangement that is useful for squeezed-light noise reduction and quantum nondemolition measurement.1 This device is pumped by a beam with a Gaussian spatial mode profile and acts on an input mode with a corresponding spatial profile. High parametric gain is required to achieve large squeezed noise reduction or accurate quantum measurement of a quadrature component of an input field. At large gains (>3 dB) the spatial variation of the pump field causes the parametrically amplified and deamplified quadrature field components to assume strongly non-Gaussian spatial profiles and to be distorted significantly with respect to each other. We analyze this distortion in the classical limit for an input beam with Gaussian profile and find that the gain measured by homodyne or direct detection differs from the low-gain limit. In the quantum limit, the case of squeezing is considered. It is shown that, in addition to the classical modifications, noise from higherorder spatial modes are coupled into the Gaussian mode, which is measured by a homodyne detection scheme using a Gauss- ian-profile local-oscillator beam. This high- gain mode-coupling process limits the degree of squeezing that can be obtained and the accuracy for quantum nondemolition measurement.

DOI
10.1364/oam.1990.fbb1

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The single-pass parametric downconver- sion amplifier is a simple optical arrangement that is useful for squeezed-light noise reduction and quantum nondemolition measurement.1 This device is pumped by a beam with a Gaussian spatial mode profile and acts on an input mode with a corresponding spatial profile. High parametric gain is required to achieve large squeezed noise reduction or accurate quantum measurement of a quadrature component of an input field. At large gains (>3 dB) the spatial variation of the pump field causes the parametrically amplified and deamplified quadrature field components to assume strongly non-Gaussian spatial profiles and to be distorted significantly with respect to each other. We analyze this distortion in the classical limit for an input beam with Gaussian profile and find that the gain measured by homodyne or direct detection differs from the low-gain limit. In the quantum limit, the case of squeezing is considered. It is shown that, in addition to the classical modifications, noise from higherorder spatial modes are coupled into the Gaussian mode, which is measured by a homodyne detection scheme using a Gauss- ian-profile local-oscillator beam. This high- gain mode-coupling process limits the degree of squeezing that can be obtained and the accuracy for quantum nondemolition measurement.
The generation of squeezed light in a single-pass parametric amplifier pumped by Gaussian beams is analyzed. Limits to the degree of squeezing that can be obtained are found that arise from spatial distortion of the signal beam that is significant for parametric gains greater than 3 dB. It is found that squeezing is limited to approximately 6 dB for typical experimental configurations. These limits severely constrain the design of quantum noise experiments unless high finesse cavities or waveguides are used.
The quantum statistics of a laser result in noise when measurements of the beam are made. This noise sets a classical limit beyond which a laser cannot be used with increasing sensitivity. This quantum noise limit is imposed on many of the uses of lasers currently, especially in power limited devices such as optical communications. The statistics of the laser photon field can be modified to produce a non-classical state resulting in lower noise than the quantum noise limit when detected appropriately. This state, called a squeezed state, has been measured previously from a cavity enhanced optical parametric oscillator (OPO) only at frequency sidebands within the linewidth of the cavity. ¶ This thesis reports measurements of squeezing at microwave frequency sidebands on an optical beam produced by an optical parametric oscillator. This is the first reported measurement of squeezing at frequency sidebands at higher longitudinal modes of the cavity from an OPO. Noise reduction below the quantum noise limit is measured at sideband frequencies of 5 MHz, 1.7 GHz, 3.4 GHz and 5.1 GHz, corresponding to the zeroth, first, second and third longitudinal modes from the squeezed beam. These results are the highest frequency sideband measurements of squeezing to date. In addition to measuring squeezing at different longitudinal modes for the fundamental Gaussian spatial mode, non-classical noise reduction is measured at the same frequencies for a squeezed higher order spatial mode, TEM10. ¶ A single mode theoretical model of the OPO is presented, based on the work of ref. [1]. Computer simulations of the squeezing predicted by this model are developed and compared to the experimental results, showing excellent agreement between the different longitudinal modes for each of the two spatial modes measured.
Summary form only given. The generation of quantum states of light, such as squeezed states, often relies on degenerate optical parametric amplification. The input signal in a degenerate optical parametric amplifier (DOPA) may be amplified or deamplified depending on the phase of the signal field relative to that of the pump field (/spl Delta//spl phi/=/spl phi//sub pump/-2/spl phi//sub signal/). We present the results of an accurate numerical DOPA model for the generation of amplitude-squeezed light with Gaussian pump and signal beams. We find that the widely accepted 3-dB limit imposed by the Gaussian beam profiles can actually be exceeded in the tight focusing regime.
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.
Noise suppression across multiple spatial modes of a light field would serve to improve the field's imaging capabilities and allow it to act as a more effective carrier \nof quantum information. This thesis describes a scheme that utilises a nonlinear process (four wave mixing (4WM)) in Rubidium 85 in order to generate a single beam of \nlight that demonstrates sub quantum noise limit (QNL) quadrature fluctuations of up to -4dB across a multitude of spatial modes simultaneously. \n \nIncluded is a description of sub-QNL (squeezed) light, followed by a breakdown of how this 4WM arrangement generates the desired quantum noise suppression. Analysis \nhas been performed that displays explicitly how the phase matching arrangement that maximises the noise suppression differs from that which optimises the efficiency of the process. This consideration is crucial to understanding why the setup achieves the levels of squeezing observed despite the presence of a strong absorption feature. \n \nFinally, the multi-spatial-mode nature of the generated squeezing is observed directly via homodyne detection using local oscillators with a range of transverse profiles. These profiles select the mode of the signal to be analysed and as such the ability to detect squeezing using a range of them demonstrates its presence across all of these modes simultaneously.
We investigate the behavior of squeezing in combined quadratures of biphotons generated in the parametric downconversion process for partially coherent pump beams in spatial, temporal, and spatiotemporal domains compared to fully coherent beams. These beams involve both stationary (continuous-wave) and non-stationary (pulsed) processes. This study also involves the derivation of complex Gaussian representation for a partially spatially coherent pump modeled as a Gaussian Schell model beam, which is more resistant to the effects of turbulence. Our findings illustrate that by employing the partially coherent pump, one can generate a squeezed state possessing partially coherent properties without compromising in squeezing by optimizing pump field amplitude, interaction length, and degree of coherence of the pump. We anticipate these results to be useful in limiting the possibility of eavesdropping in noisy channels and optical high-precision measurements in the case of continuous-variable quantum key distribution based on two-mode squeezed states.