High Sensitive Position Sensor based on PDH technique

Team members

Angela Anna Baiju and Chenyue Gu

Idea

This project is aiming of using Pound–Drever–Hall (PDH) technique to sense the vibration and the movement of the mirror driven by the noise from the environment (acoustic, thermal, etc.).

Pound–Drever–Hall laser frequency stabilisation is a powerful technique providing a means to stabilise the frequency of a laser to a specific reference frequency. It is commonly employed in precision measurements and experimental setups where precise control over the laser frequency is required, such as interferometric gravitational-wave detector. Alternatively, if a stable laser is available, the PDH technique can be used to stabilise and/or measure the instabilities in an optical cavity length via the error signal readout from the cavity.

Pound-Drever-Hall Method

The idea behind the PDH method is simple: A laser’s frequency is measured with a Fabry–Perot cavity, either transmission or reflection, and then is fed back to the input laser to suppress frequency fluctuations. The process begins with modulating the laser light. This is typically achieved by imposing a high-frequency (radio frequency or microwave) signal onto the laser beam (Local Oscillator). This modulation creates sidebands around the carrier frequency of the laser light. These sidebands are symmetrically spaced around the carrier frequency. The modulated laser light then passes through an electro-optic modulator (EOM). The EOM applies phase modulation to the light, causing the sidebands to shift in frequency relative to the carrier frequency. The amount of phase modulation applied determines the frequency separation between the carrier and the sidebands. The phase-modulated laser light is directed onto a frequency reference, which can be a stable Fabry–Perot cavity. The reflected beam is then picked off and compared with the local oscillator's signal via a mixer. The reflected light then interferes with the original laser light. This interference produces a beat signal containing frequency information about the difference between the laser frequency and the reference frequency. This beat signal is detected and processed to extract an error signal. Or if using the transmitted light Feedback Control: The error signal is used in a feedback loop to adjust the laser's frequency. The feedback loop typically involves a control mechanism, such as adjusting the current supplied to the laser diode or controlling the frequency of the modulation signal. The feedback loop aims to minimize the error signal by stabilizing the laser frequency to match the reference frequency.

The measurement is made using a form of nulled lock-in detection, which decouples the frequency measurement from the laser’s intensity. An additional benefit of this method is that the system is not limited by the response time of the Fabry – Perot cavity. You can measure, and suppress, frequency fluctuations that occur faster than the cavity can respond.

Modulation: The process begins with modulating the laser light. This is typically achieved by imposing a high-frequency (RF or microwave) signal onto the laser beam. This modulation creates sidebands around the carrier frequency of the laser light. These sidebands are symmetrically spaced around the carrier frequency. Phase Modulation: The modulated laser light then passes through an electro-optic modulator (EOM). The EOM applies phase modulation to the light, causing the sidebands to shift in frequency relative to the carrier frequency. The amount of phase modulation applied determines the frequency separation between the carrier and the sidebands. Frequency Shifting: The phase-modulated laser light is directed onto a frequency reference. This reference can be a stable Fabry–Pérot cavity or an atomic transition. The frequency reference reflects a portion of the incident light back toward the laser. Interference and Error Signal Generation: The reflected light interferes with the original laser light. This interference produces a beat signal containing frequency information about the difference between the laser frequency and the reference frequency. This beat signal is detected and processed to extract an error signal. Feedback Control: The error signal is used in a feedback loop to adjust the laser's frequency. The feedback loop typically involves a control mechanism, such as adjusting the current supplied to the laser diode or controlling the frequency of the modulation signal. The feedback loop aims to minimize the error signal by stabilizing the laser frequency to match the reference frequency.

Modification to the Project

In this project, we will lock the cavity by reading the error signal of reflection/transmission of the cavity and then feed it back to the input mirror, moving the mirror with a PZT. And then we can read out the cavity length change from the error signal. This sensing technique is commonly using in LVK (LIGO-Virgo-KAGRA) interferometric gravitational wave detection community, as well as quantum optomechnics.

Setup

We plan for a setup.... (the whole setup and explain how we applied the PDH locking)