Accurate time-delay measurement has become a crucial issue for space positioning experiments which require increasing precision over large distances. The femtosecond frequency comb has been found to be a good source for its advantages of a large nonambiguity range and coherence length up to tens of kilometers or more. A scheme combining homodyne detection and frequency combs was proposed [B. Lamine et al., Phys. Rev. Lett. 101, 123601 (2008)] that leads to a timing sensitivity reaching the shot-noise limit; with a squeezed frequency comb as the input field, the measured timing sensitivity can be further improved to the level of the sub-shot-noise limit. Based on this scheme and a squeezed frequency comb that was measured to have a phase squeezing of 1.5 dB at an analyzing frequency of 2 MHz, a narrow-band interferometric timing measurement is implemented. The minimum measurable timing variation modulation at 2 MHz is reduced from a shot-noise-limited value of $(2.8\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}$ s to $(2.4\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}$ s.
Accurate time-delay measurement has become a crucial issue for space positioning experiments which require increasing precision over large distances. The femtosecond frequency comb has been found to be a good source for its advantages of a large nonambiguity range and coherence length up to tens of kilometers or more. A scheme combining homodyne detection and frequency combs was proposed [B. Lamine et al., Phys. Rev. Lett. 101, 123601 (2008)] that leads to a timing sensitivity reaching the shot-noise limit; with a squeezed frequency comb as the input field, the measured timing sensitivity can be further improved to the level of the sub-shot-noise limit. Based on this scheme and a squeezed frequency comb that was measured to have a phase squeezing of 1.5 dB at an analyzing frequency of 2 MHz, a narrow-band interferometric timing measurement is implemented. The minimum measurable timing variation modulation at 2 MHz is reduced from a shot-noise-limited value of (2.8\ifmmode±\else\textpm\fi0.1)\ifmmode×\else\texttimes\fi10\ensuremath−20 s to (2.4\ifmmode±\else\textpm\fi0.1)\ifmmode×\else\texttimes\fi10\ensuremath−20 s.
Summary form only given. Optical techniques are widely used in many areas of science and technology to make accurate measurements. The precision of these measurements suffers from limits due to the unavoidable quantum fluctuations of light. When the light is in the quasi-classical coherent state, this limit is called ”standard quantum limit” and scales as 1/√N with N the number of photons. While better scaling can be achieved with exotic quantum states, coherent light is experimentally interesting as we are able to produce it with large N. We consider light as a probe for the measurement of a parameter p that affects the medium or the length through which the light propagates. We derived the ultimate limit of sensitivity, the so-called quantum Cramér-Rao bound, for the measurement of p [1]: for u(ω, p) the normalized mean field mode of the light, the minimal fluctuation of p that can be measured is given in Fig. 1. We also showed that this ultimate limit of sensitivity can be reached experimentally in a homodyne detection scheme, where the intense local oscillator is taken in the mode wp o ∂u ∂p, called detection mode associated with p. This measurement scheme can be applied to space-time positioning experiments such as ranging or clock synchronization [2]. The basic method for space-time positioning relies on the exchange of regular light pulses between two emitters. For coherent broadband light pulses, such as the ones delivered by a mode-locked femtosecond laser, of central frequency ω0 and of spectral width Δω, the quantum limits of the measurements of the delay t are given by δtphase = 2√Nω0 1 for interferometric measurements and δttof = 2√NΔω 1 for time-of-flight measurements. However, these two methods do not reach the quantum Cramer-Rao bound; this ultimate limit is achieved by a homodyne detection with local oscillator w(ω) o iωu(ω), and is given by 1 δtmin = (1) 2√N . Δω2 + ω2 0 For usual characteristics of a Titane:Sapphire femtosecond laser and 1 ms integration time, δtmin = 10-23s. We demonstrate this limit experimentally by using pulse shaping techniques to shape the local oscillator in the detection mode. We also study the influence of the intensity and phase noise of a mode-locked femtosecond laser on this limit. This technique can also be applied in the case of ranging in a dispersive medium such as air. In this case, dispersive effects due to environmental parameters such as pressure, temperature or humidity affect the precision of measurements. Usually, this problem is tacked by measuring separately the environmental parameters or using several wavelengths, which can be difficult and require post-processing. We show that using the same technique as previously shown, the parasitic effects due to the medium in a distance measurement can be canceled by shaping properly the local oscillator [3]: we choose for the local oscillator a mode that is orthogonal to the environmental effects, so the homodyne detection is insensitive to them, at the expense of a lower sensitivity. This scheme is an all-optical and real-time measurement of distance in a dispersive medium.
The advent of stable, highly squeezed states of light has generated great interest in the gravitational wave community as a means for improving the quantumnoise- limited performance of advanced interferometric detectors. To confidently measure these squeezed states, it is first necessary to measure the shot-noise across the frequency band of interest. Technical noise, such as non-stationary events, beam pointing, and parasitic interference, can corrupt shot-noise measurements at low Fourier frequencies, below tens of kilo-Hertz. In this paper we present a qualitative investigation into all of the relevant noise sources and the methods by which they can be identified and mitigated in order to achieve quantum noise limited balanced homodyne detection. Using these techniques, flat shot-noise down to Fourier frequencies below 0.5 Hz is produced. This enables the direct observation of large magnitudes of squeezing across the entire audio-band, of particular interest for ground-based interferometric gravitational wave detectors. 11.6 dB of shot-noise suppression is directly observed, with more than 10 dB down to 10 Hz.
The advent of stable, highly squeezed states of light has generated great interest in the gravitational wave community as a means for improving the quantumnoise- limited performance of advanced interferometric detectors. To confidently measure these squeezed states, it is first necessary to measure the shot-noise across the frequency band of interest. Technical noise, such as non-stationary events, beam pointing, and parasitic interference, can corrupt shot-noise measurements at low Fourier frequencies, below tens of kilo-Hertz. In this paper we present a qualitative investigation into all of the relevant noise sources and the methods by which they can be identified and mitigated in order to achieve quantum noise limited balanced homodyne detection. Using these techniques, flat shot-noise down to Fourier frequencies below 0.5 Hz is produced. This enables the direct observation of large magnitudes of squeezing across the entire audio-band, of particular interest for ground-based interferometric gravitational wave detectors. 11.6 dB of shot-noise suppression is directly observed, with more than 10 dB down to 10 Hz.
We propose and experimentally demonstrate a quantum-enhanced fiber Mach-Zehnder interferometer for low-frequency phase measurement beyond the shot-noise limit using a high-frequency squeezing technique. The local oscillator field is amplitude-modulated in the MHz range and is then demodulated to avoid the technical noise that occurs at low frequencies. After measurement of the phase noise at a frequency of tens of kHz, an improvement of ∼2 dB relative to the shot-noise level is achieved. Additionally, the amplitude modulation depth has no significant effect on the phase noise improvement of the interferometer when deployed in our experimental configuration. The current scheme introduces a quantum technique into the fiber-based measurements, particularly for the low frequency range, and this scheme has potential applications in the high-precision fiber sensing of temperature, strain, and various other parameters.
Improvements in precision beyond the limit set by the vacuum state or zero-point fluctuations of the field are reported for two optical experiments. Both experiments employ the squeezed light from an optical parametric oscillator to reduce the level of fluctuations in one of two quadrature phase amplitudes below the shot-noise level (SNL). The first experiment follows the work of Caves1 on precision interferometry with squeezed states. An increase in signal-to-noise of 2.5 dB relative to the SNL is demonstrated for the detection of phase modulation in a Mach-Zehnder interferometer. In the second experiment amplitude modulation is encoded on a weak signal beam with an acoustooptic modulator. For the case of a squeezed signal beam compared with a beam in a coherent state, an improvement in sensitivity of 2.5 dB is achieved for the detection of amplitude changes of the field. The observed increases in sensitivity in both experiments are currently limited by simple linear losses in propagation and detection and not by the degree of available squeezing.