A general formalism is developed for optimizing homodyne detection of quadrature-noise squeezing by selection of the local-oscillator (LO) field. The optimum LO is the minimum-eigenvalue eigenfunction of a particular Fredholm integral equation whose kernel depends on the signal field's normally ordered and phase-sensitive covariance functions. The squeezing that results from use of the optimum LO equals one plus twice its associated eigenvalue. A continuous-wave (cw) simplification of the general formalism is presented for the case of stationary signal-field covariances when the homodyne photocurrent is spectrum analyzed. Another simplified special case is exhibited for single-spatial-mode operation, such as is encountered in fiber-based quantum-noise experiments. The cw-source–spectrum-analysis approach is used to determine the optimum LO field and its squeezing performance for cw squeezed-state generation in a bulk Kerr medium with a Gaussian spatial-response function. The single-spatial-mode framework is employed to find the optimum LO field and its squeezing performance for pulsed squeezed-state generation in a single-mode optical fiber whose Kerr nonlinearity has a noninstantaneous response function. Comparison of the cw limit of this pulsed analysis with previous cw fiber-squeezing theory reveals a new regime for quadrature-noise reduction: Raman squeezing in fiber four-wave mixing.
A general formalism is developed for optimizing homodyne detection of quadrature-noise squeezing by selection of the local-oscillator (LO) field. The optimum LO is the minimum-eigenvalue eigenfunction of a particular Fredholm integral equation whose kernel depends on the signal field's normally ordered and phase-sensitive covariance functions. The squeezing that results from use of the optimum LO equals one plus twice its associated eigenvalue. A continuous-wave (cw) simplification of the general formalism is presented for the case of stationary signal-field covariances when the homodyne photocurrent is spectrum analyzed. Another simplified special case is exhibited for single-spatial-mode operation, such as is encountered in fiber-based quantum-noise experiments. The cw-source–spectrum-analysis approach is used to determine the optimum LO field and its squeezing performance for cw squeezed-state generation in a bulk Kerr medium with a Gaussian spatial-response function. The single-spatial-mode framework is employed to find the optimum LO field and its squeezing performance for pulsed squeezed-state generation in a single-mode optical fiber whose Kerr nonlinearity has a noninstantaneous response function. Comparison of the cw limit of this pulsed analysis with previous cw fiber-squeezing theory reveals a new regime for quadrature-noise reduction: Raman squeezing in fiber four-wave mixing.
The detection of squeezed optical fields generated by intracavity nonlinear-optical interactions is described. The relationship between quantum-statistical properties of the cavity mode and those of the field at a detector placed outside the cavity discussed. The detected field is composed of a source field from the cavity plus a free external field. The free field couples weakly to the cavity so that it is correlated with the source field. The photocurrent spectrum in optical homodyne detection is calculated, and the spectrum of squeezing is defined. This spectrum can be calculated entirely in terms of intracavity fields without requiring knowledge of the correlations between source and free-field contributions in the cavity output. This follows from an explicitly normally ordered, time-ordered treatment of the photodetection problem. Contrasting earlier treatments of photodetection for squeezed fields, in a normally ordered approach, shot noise arises naturally from the self-correlation of photocurrent for pulses. The derived spectrum is converted into nonnormally ordered, non-time-ordered form to recover the results of these earlier treatments and their interpretation of shot noise in terms of local-oscillator quantum noise, signal and quantum noise, and detector-efficiency quantum noise.
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.
The spatial character of the noise on a light field affects its usefulness for imaging. Multi-spatial-mode (MSM) squeezed light has noise below the quantum noise limit in multiple spatial modes, and can be used for super resolution imaging. The generation of such light has long been an experimental goal within the field of quantum optics. \n \nThis work introduces the theory behind the generation of squeezed light, and its measurement using a homodyne detector. A four-wave mixing process in a rubidium 85 vapour is used to experimentally generate squeezed light. The properties of this squeezed light are investigated, through the use of homodyne detection with a bichromatic LO. \n \nThis thesis further investigates how the squeezed quadrature changes from amplitude to phase over a range of 40 MHz. The MSM nature of a squeezed light field is directly investigated. The field is shown to contain at least 75 squeezed spatial modes in the frequency domain, each squeezed at a level of up to -2.5 dB. This thesis develops techniques to measure the spatial character of noise on a light field in the time domain. These are promising techniques for the analysis of the MSM nature of a squeezed light in the time domain.
Quantum noise is one of the limiting factors in laser-interferometric gravitational-wave (GW) detectors. The application of squeezed states in these interferometers allows the reduction of quantum noise in one quadrature. Due to opto-mechanical coupling in a GW detector the squeezed quadrature needs to be rotated within the spectrum to achieve a broadband noise reduction. So far, the implementation of additional filter cavities is considered that allow for the optimal, frequency-dependent rotation of the squeezed quadrature. However, these cavities need to have low loss, a length in the order of \unit[100]{m} and must be situated in the vacuum system, making them cost-intensive. In 2017, Ma and coworkers proposed a scheme for the broadband quantum-noise reduction without the need of additional filter cavities. It was shown by Brown et al. that a similar scheme can be used to broadband-enhance interferometers with a detuned signal-recycling cavity. Here, we performed a proof-of-principle experiment of the proposal on a table-top-scale. Squeezed states were produced detuned to the carrier field of a \unit[2.5]{m}-linear cavity and read out in a bichromatic homodyne detection. The frequencies of the lower and upper local oscillator were at entangled sidebands of the squeezed field. Depending on the relations between the involved frequencies, we can address both variants of the proposal. We show, that the frequency-dependences of the resulting noise spectra fit to a theoretical model we derived from the theory used by Ma et al. With this work we set the path towards an implementation of these schemes in a GW-detector prototype, where the compatibility of the approach with a low-frequency suspended interferometer can be tested. Moreover, we used the same setup to show nonclassical interferometer enhancement at low frequencies by high-frequency squeezed states. Here, a heterodyne readout scheme was implemented to avoid limiting noises at low frequencies. The application of squeezed states centered around the local oscillator frequency yielded an improvement in signal-to-noise ratio of $\unit[3.4]{dB}\pm\unit[0.3]{dB}$. Additionally, I designed, built and characterized a compact source of squeezed vacuum-states at \unit[1064]{nm} with a footprint of just $\unit[0.8]{m^2}$. I show measurements of squeezed states from this source with a reduction of quantum noise of $\unit[10.7]{dB}\pm\unit[0.2]{dB}$ below the vacuum noise and present a noise reduction in the frequency range from \unit[70]{kHz} to \unit[65]{MHz}.
We demonstrate the methods for increasing the observed squeezing level in the generation of squeezed states of light at 1064 nm with periodically poled KTiOPO4 (PPKTP) crystal. We analyze the technical limits to the reduction of noise in the squeezed quadrature theoretically, including the intra-cavity loss of the optical parametric amplifier (OPA) cavity, the normalized amplitude, the detection frequency, and the mode matching on the balanced homodyning stage. To observe a high degree of squeezing, we improve the quality of mode matching into the OPA cavity and the mode cleaning (MC) cavity experimentally. By optimizing mode matching of the light into cavities, the finesse of the cavities would be higher in practice and the desirable spatial mode can be realized. As the intensity noise of the laser light reach the shot noise limit above the frequency of 1 MHz, which is sufficient for our experiment, so the MC cavity is incorporated to filter higher-order transverse modes of the local oscillator (LO) beam for the balanced homodyne detection. The experimental and theoretical results show that it is essential to optimize the mode matching efficiency to generate and detect high degree of squeezing otherwise an inefficiency mode matching will throw away the squeezing and transform the squeezed field into a vacuum field.
We experimentally study a homodyne detection technique for the characterization of a quadrature squeezed field where the correlated bands, here created by four-wave mixing in a hot atomic vapor, are separated by a large frequency gap of more than 6 GHz. The technique uses a two-frequency local oscillator to detect the fluctuations of the correlated bands at a frequency accessible to the detection electronics. Working at low detection frequency, the method allows for the determination of both the amplitude and the phase of the squeezing spectrum. In particular, we show that the quadrature squeezing created by our four-wave mixing process displays a noise ellipse rotation of π/2 across the squeezing spectrum.