Application Cases

Experiment Name: Experiment on Single-Stage Feedback Noise Suppression Based on an Electro-Optic Amplitude Modulator (EOAM)

Research Direction: This research explores the suppression mechanism of laser intensity noise and its quantum control effects in single-atom optical trapping using a single-stage feedback technique with an Electro-Optic Amplitude Modulator (EOAM). Static optical path experiments quantified the noise attenuation characteristics of the feedback loop within the 0–1 MHz frequency domain (reaching 20 dB at 100 kHz), and modulation parameters were optimized to enhance power stability (standard deviation of 0.5%). Furthermore, the quantum state control effects of noise suppression were verified in a cesium atom dipole trap: the atom lifetime increased from 0.12 s to 13.9 s (a two-order-of-magnitude improvement), and the homogeneous dephasing time T₂∗ increased from 20.7 ms to 107.5 ms (a 5-fold improvement), revealing the quantitative relationship between the intensity noise spectrum and parametric heating/quantum dephasing.

Experimental Objective: To investigate the influence of modulation parameters (bias voltage, gain bandwidth) of the single-stage EOAM feedback loop on laser intensity noise suppression, and its control effects on extending atom lifetime (by two orders of magnitude) and enhancing quantum dephasing time (by a factor of 5) in single-atom optical trapping. This aims to provide a low-noise optical trapping solution for quantum precision manipulation systems.

Test Equipment: ATA-2021H High-Voltage Amplifier, Electro-Optic Amplitude Modulator, Proportional-Integral Controller, Custom High-Numerical-Aperture Objective Lens, Cesium Atom Magneto-Optical Trap (MOT) System, Single-Photon Avalanche Diode (SPAD/SPCM), Microwave Source, Microwave Amplifier, Polarizing Beam Splitter (PBS), Quarter-Wave Plate (QWP), Half-Wave Plate (HWP), Spectrum Analyzer, Oscilloscope, Fiber Coupling System.

Experimental Process:

Figure 1: Experimental setup diagram for laser intensity noise suppression in the 0-1 MHz range using a combination of an Acousto-Optic Modulator (AOM) and an Electro-Optic Modulator (EOM).

Figure 2: Diagram of the experimental setup for single-stage feedback loop noise suppression.

Figure 3: Physical image of the single-stage feedback loop noise suppression apparatus.

Within a static optical system, a spectrum analyzer (DC-150 MHz) was used to quantify the suppression effect of the single-stage EOAM feedback loop on 1064 nm laser intensity noise (bias voltage 0 V, gain bandwidth 1 MHz). The noise power spectrum was inverted to derive a theoretical model for the parametric heating rate within the 0–500 kHz frequency domain. Simultaneously, within a combined cesium atom MOT-dipole trap system, trapping light with suppressed noise (power 11.6 mW, trap depth 0.34 mK) was applied. The atom survival probability was monitored using a single-photon counting module (SPCM, count rate 100 counts/50 ms), in conjunction with microwave pulse sequences (π/2-τ-π-τ pulses, frequency 9.192 GHz, power 10 W) driving Ramsey interference and spin echo measurements. Exponential decay fitting was employed to extract the atom lifetime T₁ and the homogeneous dephasing time T₂∗, establishing a quantitative control model linking laser intensity fluctuations to atomic dephasing.

Experimental Results:

Figure 4: (a) Atom heating rate in the trap with the feedback loop open and closed. (b) Atom lifetime with the feedback loop open and closed.

Figure 5: Atom dephasing time in the trap with the noise suppression loop open and closed.

Noise suppression tests showed that when the feedback loop was closed (bias voltage fixed at 0 V), the laser intensity noise was attenuated by 20 dB at 100 kHz, and the standard deviation of power fluctuations decreased to 0.5% (compared to 11% in free-running operation). The theoretical parametric heating rate decreased from 6.35 s⁻¹ to 0.05 s⁻¹. Atom trapping experiments confirmed: without noise suppression, the atom lifetime was only 0.12 s (dominated by heating-induced escape); with feedback applied, the lifetime extended to 13.9 s (a 116-fold improvement), with 27 dB noise suppression observed at the axial oscillation frequency of 2.34 kHz. Quantum coherence measurements revealed: the dephasing time T₂ for free evolution (Ramsey interference) increased from 4.84 ms to 8.54 ms, while the homogeneous dephasing time T₂∗ resolved by spin echo techniques improved from 20.7 ms to 107.5 ms (a 420% increase). Furthermore, the amplitude decay rate of the spin echo after noise suppression decreased by a factor of 4.5. 

Amplifier Efficacy in this Experiment: The high-voltage amplifier was used to boost the milliwatt-level error signal from the proportional-integral controller to the hundred-volt level, driving the electro-optic amplitude modulator to achieve real-time modulation of laser intensity. This ensured the feedback loop's dynamic response on the hundred-microsecond scale for suppressing intensity noise in the 0–1 MHz range.

Recommended Voltage Amplifier – ATA-2021B High-Voltage Amplifier:

Figure: ATA-2021B High-Voltage Amplifier specifications.