Traditional locking techniques, such as PDH (Pound-Drever-Hall), HC (Hansh-Couillaud), spatial mode interference technique, offset sideband locking technique, quantum noise locking, etc., have been widely applied to laser frequency stabilization and precision optical interferometry measurement. Here, a new technique, which we call phase-sensitive heterodyne locking (PSHL), is investigated by use of frequency-synthesized light to obtain a phase-sensitive high-frequency photoelectric readout to lock the phase of a squeezed light. Comparing with above techniques, there are several kinds of advantages for PSHL to be advocated. Frequency-synthesized light, which allows arbitrary control of the amplitudes and phases of the modulation sidebands relative to the carrier, is derived by the AOM (acousto-optic modulator), not the EOM (electro-optic modulator). Interferometic signals coming from a balanced heterodyne detector are high-frequency AC photoelectric current which can easily get rid of low-frequency classical noise and lead to reach or break through the shot noise limit. A theoretical derivation of the PSHL error signal and the associated stability of the squeezed and anti-squeezed lock points will be carried out in this work.
Traditional locking techniques, such as PDH (Pound-Drever-Hall), HC (Hansh-Couillaud), spatial mode interference technique, offset sideband locking technique, quantum noise locking, etc., have been widely applied to laser frequency stabilization and precision optical interferometry measurement. Here, a new technique, which we call phase-sensitive heterodyne locking (PSHL), is investigated by use of frequency-synthesized light to obtain a phase-sensitive high-frequency photoelectric readout to lock the phase of a squeezed light. Comparing with above techniques, there are several kinds of advantages for PSHL to be advocated. Frequency-synthesized light, which allows arbitrary control of the amplitudes and phases of the modulation sidebands relative to the carrier, is derived by the AOM (acousto-optic modulator), not the EOM (electro-optic modulator). Interferometic signals coming from a balanced heterodyne detector are high-frequency AC photoelectric current which can easily get rid of low-frequency classical noise and lead to reach or break through the shot noise limit. A theoretical derivation of the PSHL error signal and the associated stability of the squeezed and anti-squeezed lock points will be carried out in this work.
The shot-noise-limited sensitivity for detecting audio-frequency phase signals has garnered significant interest in both research and practical applications. This work presents a novel experimental setup that generates frequency-synthesized light with suppressed carrier and enhanced sidebands using an electro-optic intensity modulator (EOIM). When injected into a Mach-Zehnder interferometer (MZI), the EOIM-generated light not only enables phase-sensitive heterodyne locking to stabilize the relative phase of the MZI but also functions as a balanced heterodyne detector for audio-frequency phase measurements. By integrating these three key techniques into the MZI, phase detection sensitivity reaches the shot-noise limit across the audio-frequency band. This advancement holds promise for applications in gravitational wave detection, vacuum magnetic birefringence studies, spin-orbital interactions, material characterization, polarization microscopy, atomic magnetometry, and biomedical optics.
Quantum optical states which have no coherent amplitude, such as squeezed vacuum states, can not rely on standard readout techniques to generate error signals for control of the quadrature phase. Here we investigate the use of asymmetry in the quadrature variances to obtain a phase-sensitive readout and to lock the phase of a squeezed vacuum state, a technique which we call noise locking (NL). We carry out a theoretical derivation of the NL error signal and the associated stability of the squeezed and anti-squeezed lock points. Experimental data for the NL technique both in the presence and absence of coherent fields are shown, including a comparison with coherent locking techniques. Finally, we use NL to enable a stable readout of the squeezed vacuum state on a homodyne detector.
The Pound--Drever--Hall (PDH) technique is routinely used to stabilize the frequency of a laser to a reference cavity. Electronic sideband (ESB) locking, a PDH variant, bridges the frequency gap between the discrete cavity resonances and a desired laser frequency. Here we use quadrature amplitude modulation (QAM), a standard technique in digital communications, to generate the high-quality phase-modulated radio-frequency (rf) drive required for ESB locking. We develop a theoretical framework to analyze how in-phase/quadrature-phase (I/Q) impairments distort the ESB error signal and induce frequency offsets relevant to ultranarrow-linewidth lasers. We then design and implement a direct software-defined radio (SDR) on an UltraScale+ RFSoC platform, frequently adopted across modern quantum-computing systems, to digitally compensate QAM I/Q impairments. Using this device, we generate phase-modulated rf signals with a large phase-modulation index of 1.01 rad and root-mean-square I/Q errors below 0.3% over a carrier-frequency range of 350MHz to 1.75GHz. Finally, we lock a laser to an ultralow expansion (ULE) reference cavity and demonstrate continuous laser-frequency tuning by ramping the carrier frequency while maintaining lock, validating the continuous tunability of our ESB locking instrument.
We present a cavity-enhanced optical absorption measurement technique based on high-bandwidth Pound-Drever-Hall (PDH) sideband locking, which naturally provides a real-time, resonant amplitude quadrature readout that can be mapped onto the cavity’s internal loss rate. Cavity-enhancement is widely used in the detection of small signals -- an optical cavity traps photons between two highly reflective mirrors, thereby enhancing the effective path length through the absorber [Romanini et al., 2014]. Most of the available techniques, however, probe transmission signals and/or do not provide the stability required for the detection of fast signals.To ensure optimal enhancement of absorption sensitivity, probe light must be locked on resonance with the cavity. PDH locking relies on phase modulation of a laser beam, creating two sidebands on the original carrier frequency [Black, 2001]. Upon reflection from a cavity, this modulated light produces a heterodyne signal (beat note) that can be detected and demodulated. We use the phase quadrature of the beat note to lock the cavity on resonance with one of the sidebands, achieving a locking bandwidth in the MHz range that keeps cavity and probe light resonant for hours [Reinhardt et al., 2017]. Simultaneously, we monitor the amplitude quadrature, which provides a continuous, real-time, heterodyne-amplified readout of the cavity’s internal absorption. Our PDH sideband cavity-enhanced absorption readout technique (SideCAR) ensures high sensitivity without reaching saturation limits in the intracavity medium by keeping a relatively low intracavity power, since only one of the sidebands is allowed to enter the cavity, but the signal is boosted above the detector noise by heterodyne detection (using the carrier as a local oscillator).This thesis presents the theoretical formulation of the sensing technique together with the expressions for the sensitivity limit (ultimately given by the laser quantum noise), and the experimental results from a test cavity setup. Probing a proof-of-concept 5-cm-long Fabry-Perot cavity with a coupled power of 160 uW, we measure an absorption sensitivity of 7*10^(-11) cm^(-1)/sqrt(Hz) at 100 kHz (roughly the cavity bandwidth), a factor of 11 from the shot-noise limit. This technique allows the detection of small, transient signals against absorptive backgrounds with sensitivity close to the shot noise limit using a reflection-based measurement in a fairly simple setup, opening the possibility of developing new microscopic single-port real-world sensors for transients, for example using micron-scale optical fiber cavities
Current interferometric gravitational wave detectors were designed to be limited, in much of their sensitive
band, by quantum noise in the form of shot noise (at high frequency) or quantum radiation pressure noise
(at low frequency). In the current observation run (O3), a squeezed light source has been used to
manipulate quantum noise and surpass the limits imposed by the circulating laser power by injecting nonclassical states of the electromagnetic field, called squeezed vacuum states, in the interferometer's dark
port. Recent O3 results show that this technique was able to reduce the shot noise contribution to the
noise spectral density by about one half. To surpass the so called standard quantum limit across the entire
sensitivity band, an even more complex variation of this technique will be implemented, which requires the
use of a so called “filter cavity” to reflect the squeezed quantum field and rotate the squeezing angle as a
function of frequency.
The performance of this techniques is however severely limited by light losses. One big contributor to
optical losses is the mismatch between the squeezed vacuum beam, the beam circulating into the
interferometer and, in the near future, the filter cavity fundamental transverse spatial mode.
To be able to monitor and actively correct mode mismatch, an accurate, online sensing technique is
needed. A possible solution consists in the introduction of an Electro-Optic Lens (EOL) that can induce
radio-frequency sidebands in the Laguerre-Gauss 10 (LG10) transverse mode of the beam. If the
modulation frequency is tuned in a way that one sideband is at the cavity LG10 frequency, then the
resonance breaks the symmetry of the two sidebands and converts phase modulation into amplitude
modulation, making it possible to retrieve an error signal directly from the cavity reflected electric field
with the same single-element photodetector used for the Pound Drever Hall (PDH) locking technique. This
error signal carries information about the magnitude and nature of the mismatch, providing all is needed to
inform a dedicated feedback loop with a suitable actuator to maintain the mismatch at or below the 1%
level.
The goal of this thesis is to demonstrate the technique on a dedicated bench-top experiment employing an
EOL prototype device. The EOL alignment and working point, as well as the cavity lock parameters were
optimized in an already existing setup. Simulations and theoretical calculations of the cavity reflected field
were performed to evaluate the system non-idealities: both Electro-Optic Modulator (for PDH technique)
and EOL modulations effects and interactions, as well as some system imperfections were considered. The
simulations confirm that this technique requires a stable cavity lock condition, and for this reason an
accurate study and optimization of the feedback loop parameters was done. In conclusion, a
characterization of the EOL error signal response to different mismatch conditions are presented.
As part of the effort to make use of squeezed states of light for detection of sub-shot-noise optical signals, we study the balanced heterodyne scheme, for which the corresponding spectral density of the photocurrent fluctuations produced at the output of the detector is calculated as the Fourier transform of their autocorrelation function. Our analysis shows that, for maximal signal-to-noise ratio enhancement by use of squeezed states of light, an optical signal to be measured must be carried in the squeezed quadrature of the carrier field. We discuss how "the additional heterodyne noise" can be eliminated in this scheme and its potential application to gravitational-wave searching. To demonstrate the practical feasibility, we propose and study a phase-locking technique for this scheme.