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Quantum control of the librations of a levitated nanoparticle
In this project the student will work with an existing standing-wave optical trap where librational modes frequencies reach the MHz frequency band to prepare a nanoparticle in the librational groundstate.
Quantum control over the motional degrees of freedom of a levitated object has been recently achieved both using passive (i.e. cavity-based) [1] and active feedback schemes [2,3]. Asymmetric levitated objects also possess well defined rotational degrees of freedom that experience restoring optical torques. As a result, the object orientation performs small angle oscillations (librations) about some equilibrium position determined by the beam polarization and by the particle optical susceptibility tensor. A growing control over the librations is underway, yet the preparation of a high purity quantum state (e.g. the groundstate) has remained an elusive task.
In this project the student will work with an existing standing-wave optical trap where librational modes frequencies reach the MHz frequency band. The student will need to:
1. Design a homodyne receiver to perform quantum limited measurements of the particle orientation and determine the absolute measurement efficiency of the apparatus.
2. Characterize an existing fast light polarization controller based on an electro optical modulator (EOM) and show that the polarization controller can be used to exert a dynamical torque on the levitated object.
3. Implement and optimize a digital feedback controller and demonstrate the capability to reduce the amplitude of the thermal librational motion in moderate vacuum.
4. Characterize the feedback cooling performance while gradually approaching ultra-high vacuum.
Provided that the radiation torque shot noise limited regime can be reached for pressures about 10-8 mBars and the measurement efficiency is above 1/9, this will allow the student to prepare the nanoparticle in the librational groundstate.
Fig.1 - Sketch of the experimental apparatus.
A Sagnac interferometer based optical tweezer traps an asymmetric nanoparticle. The outcomes of efficient quantum limited measurements of the object angular displacement are fed to a digital filter producing a feedback signal that is transduced into an optical torque by modulating the linear polarization of the trapping laser. The synthesised optical torque counteracts angular fluctuations effectively cooling the librational degree of freedom.
References:
[1] U. Delić et al. Science 367 (6480), 892-895 (2020)
[2] L. Magrini et al. Nature 595 (7867), 373-377 (2021)
[3] F. Tebbenjohanns et al. Nature 595 (7867), 378-382 (2021)
Prerequisites: Optics, Electronics, Quantum measurement theory.
Quantum control over the motional degrees of freedom of a levitated object has been recently achieved both using passive (i.e. cavity-based) [1] and active feedback schemes [2,3]. Asymmetric levitated objects also possess well defined rotational degrees of freedom that experience restoring optical torques. As a result, the object orientation performs small angle oscillations (librations) about some equilibrium position determined by the beam polarization and by the particle optical susceptibility tensor. A growing control over the librations is underway, yet the preparation of a high purity quantum state (e.g. the groundstate) has remained an elusive task. In this project the student will work with an existing standing-wave optical trap where librational modes frequencies reach the MHz frequency band. The student will need to: 1. Design a homodyne receiver to perform quantum limited measurements of the particle orientation and determine the absolute measurement efficiency of the apparatus. 2. Characterize an existing fast light polarization controller based on an electro optical modulator (EOM) and show that the polarization controller can be used to exert a dynamical torque on the levitated object. 3. Implement and optimize a digital feedback controller and demonstrate the capability to reduce the amplitude of the thermal librational motion in moderate vacuum. 4. Characterize the feedback cooling performance while gradually approaching ultra-high vacuum. Provided that the radiation torque shot noise limited regime can be reached for pressures about 10-8 mBars and the measurement efficiency is above 1/9, this will allow the student to prepare the nanoparticle in the librational groundstate. Fig.1 - Sketch of the experimental apparatus. A Sagnac interferometer based optical tweezer traps an asymmetric nanoparticle. The outcomes of efficient quantum limited measurements of the object angular displacement are fed to a digital filter producing a feedback signal that is transduced into an optical torque by modulating the linear polarization of the trapping laser. The synthesised optical torque counteracts angular fluctuations effectively cooling the librational degree of freedom.
References: [1] U. Delić et al. Science 367 (6480), 892-895 (2020) [2] L. Magrini et al. Nature 595 (7867), 373-377 (2021) [3] F. Tebbenjohanns et al. Nature 595 (7867), 378-382 (2021)