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Optics Letters

Reduction of zero baseline drift of the Pound–Drever–Hall error signal with a wedged electro-optical crystal for squeezed state generation

Zhixiu Li, Weiguang Ma, Wenhai Yang, Yajun Wang, Yaohui Zheng

Published Jul 12, 2016• 66 citations
Publisher

Abstract

as the modulation crystal to reduce the zero baseline drift (ZBD) of the Pound-Drever-Hall (PDH) error signal. When the input linear polarization is not along the modulation direction, the wedged design can separate the two orthogonal polarizations in space after the EOM and eliminate the interference between the carrier and the two orthogonal sidebands. Therefore, the residual amplitude modulation (RAM) of phase modulation process caused by the input polarization misalignment and the etalon effect can be significantly reduced. The noise power spectrum of phase-modulated light with wedged crystal EOM is suppressed from -24 to -69 dBm, which is much lower than that with conventional EOM. The peak-to-peak value of the ZBD of the PDH error signal is reduced effectively to +70/-50 ppm during the 10 h, which meets the requirements for stable squeezed light generation.

DOI
10.1364/ol.41.003331

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as the modulation crystal to reduce the zero baseline drift (ZBD) of the Pound-Drever-Hall (PDH) error signal. When the input linear polarization is not along the modulation direction, the wedged design can separate the two orthogonal polarizations in space after the EOM and eliminate the interference between the carrier and the two orthogonal sidebands. Therefore, the residual amplitude modulation (RAM) of phase modulation process caused by the input polarization misalignment and the etalon effect can be significantly reduced. The noise power spectrum of phase-modulated light with wedged crystal EOM is suppressed from -24 to -69 dBm, which is much lower than that with conventional EOM. The peak-to-peak value of the ZBD of the PDH error signal is reduced effectively to +70/-50 ppm during the 10 h, which meets the requirements for stable squeezed light generation.
Residual amplitude modulation is one of the major stability-degrading factors in many precision measurements. Using an electro-optic (EO) crystal with wedged input and output surfaces is an effective way to suppress residual amplitude modulation. Here the mechanism of residual amplitude modulation in this approach is investigated. The residual amplitude modulations measured in standard and wedged EO crystals bear similarities in their temperature and polarization dependences, implying that a mixture of the two orthogonal polarizations in the extraordinary light is responsible for the residual amplitude modulation in the wedged EO crystal. Similar to a standard EO crystal, a non-uniform spatial distribution of residual amplitude modulation is also observed in the extraordinary light emerging from the wedged EO crystal. The optical isolator after the EO crystal is replaced by a Faraday rotator, and an improvement in the long-term stability is observed. With the wedged-crystal approach, residual amplitude modulation as low as 2×10−7 is observed, contributing a frequency instability of 8×10−18 (500 s) in Pound–Drever–Hall frequency stabilization with a discrimination slope of 1×10−4 V/Hz.
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.
Laser phase noise is one of the limiting factors that dictate gate fidelities and coherence times in trapped-ion quantum systems. Previous studies have reported that when the Rabi frequency of an ion qubit is close to the servo-bump phase-noise frequency, the driving laser limits the fidelity and coherence time. This issue has typically been mitigated by choosing a Rabi frequency outside the servo-bump region. However, this constrains the usable range of gate speeds and can limit the achievable fidelity. To address this issue, we developed an active phase-noise stabilization system for a barium-ion optical-qubit laser at 1762 nm, employing a fiber electro-optic modulator (EOM) with an electrical feedforward servo. Our results demonstrate that this setup, based on the Pound-Drever-Hall (PDH) feedforward method, can suppress servo-bump phase noise by 15 dB near the bump peak frequency in our locking system. The laser phase noise is analyzed using delayed self-heterodyne interferometry (DSHI). We further tested the stabilized laser on an optical qubit and observed a clear improvement in coherence time based on the measured amplitude decay of Rabi oscillations, even when the Rabi frequency lies within the servo-bump bandwidth. This technique can be readily adapted to other optical qubits with minimal modifications.
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 1.011.011.01 rad and root-mean-square I/Q errors below 0.3 %0.3\ \%0.3 % over a carrier-frequency range of 350 MHz350~\mathrm{MHz}350 MHz to 1.75 GHz1.75~\mathrm{GHz}1.75 GHz. 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.
Residual amplitude modulation is one of the major sources of instability in ultra-sensitive optical detections based on frequency modulation. Using a MgO·LiNbO(3) electro-optic crystal, we systematically measure the temperature and polarization dependence of residual amplitude modulation and our experimental results are in good agreement with a previous theoretical analysis. After optical phase modulation, two independent arms including optical detection and frequency demodulation are employed to closely examine the instability of the residual amplitude modulation. Residual amplitude modulation below 25 ppm is obtained with an active cancellation scheme in which the crystal temperature is varied so as to zero the baseline drifts with different origins. Possible improvements for better suppression and stability are discussed.
We present a mutual compensation scheme of three phase fluctuations, originating from the residual amplitude modulation (RAM) in the phase modulation process, in the bright squeezed light generation system. The influence of the RAM on each locking loop is harmonized by using one electro-optic modulator (EOM), and the direction of the phase fluctuation is manipulated by positioning the photodetector (PD) that extracts the error signal before or after the optical parametric amplifier (OPA). Therefore a bright squeezed light with non-classical noise reduction of π is obtained. By fitting the squeezing and antisqueezing measurement results, we confirm that the total phase fluctuation of the system is around 3.1 mrad. The fluctuation of the noise suppression is 0.2 dB for 3 h.