Manipulation of an optomechanically coupled oscillator using a quantum filter
Optical interferometry enables us to obtain displacement information of an object through a phase shift of reflected electromagnetic waves. An optomechanical coupling is a naturally existing feedback system in the interferometry, which has been applied to a variety of precise measurements including quantum ground state cooling of a macroscopic object, gravitational-wave detection, and nuclear magnetic resonance. The optomechanical coupling can be tuned through an initial offset to a resonant cavity mode and it is hitherto the only way to control the feedback system. Here we propose an active feedback system using the optomechanical coupling and a quantum filter that can be made of either a non-linear crystal or a cryogenic micro-resonator. The feedback system creates a resonator called "optical spring." An additional quantum feedback loop with a non-linear crystal increases the real part of the spring, while in the foreseen conditions, a feedback loop with a cryogenic micro-resonator decreases the imaginary part of the spring. For a measurement using this spring as a probe, the former leads to signal gain enhancement and the latter leads to signal bandwidth enhancement.
Our proposal is two-sided. First we establish proof-of-principle experiments for the two different types of quantum feedback system. The signal gain enhancement will be tested at a prototype experiment in Tokyo Institute of Technology and the signal bandwidth enhancement will be tested at a cryogenic experiment in Laboratoire Kastler Brossel. Optical losses in the feedback system is a critical issue for the signal gain enhancement. Laboratoire des Matériaux Avancés will make an intense effort to lower losses in the intracavity components including a non-linear crystal. For both experiments, a classical control to locate each optics in a proper position is essential, and University of Tokyo will be in charge of this issue.
In parallel to the proof-of-principle experiments, we start new experiments or rapidly promote on-going experiments to explore an innovative application of these state-of-the-art techniques. The optomechanical coupling has been utilized in various experiments in different fields. A limited gain is almost always an issue in such experiments. A limited bandwidth is not always an issue but it can be a bottleneck after we succeed in increasing the gain to some extent. The active quantum feedback is a way to improve the performance in those experiments. We propose to demonstrate three innovative applications.
(i) Test of macroscopic quantum mechanics: The existence of a fundamental length at Planck scale leads to a modification of Heisenberg's uncertainty principle. An extremely high precision measurement of a macroscopic object is required to observe a possible deviation from conventional quantum mechanics. We propose to perform three experiments with different resonators. As possible deviations from standard quantum mechanics are expected to depend on the probed mass, a comparison of the results in our three state-of-art experiments might open a window to the quantum-classical border.
(ii) Gravitational-wave detection: Gravitational waves are ripples of spacetime generated by massive astronomical events like Black hole mergers, Supernovae, etc. A gravitational-wave detector is a km-scale Michelson interferometer with an optical resonator in each baseline. Both the signal gain and signal bandwidth enhancement can be used to improve the sensitivity of a gravitational-wave detector. A significant improvement can be expected at frequencies higher than a few kilo-Hertz where a number of valuable astrophysics sources are yet to be observed by currently operating detectors. Information of the inner core of a neutron star, for example, will be obtained through the waveform of a gravitational-wave at around 3-4 kHz. Diastrophism of a neutron star, a possible cause of pulsar glitches, can be observed with a significantly improved sensitivity.
(iii) Measurement of nuclear magnetic resonance: A simple electric LC circuit can play a role of the quantum feedback filter. Although classical thermal noise in the coil will overwrite the quantum property of our optomechanical oscillator, the change of the dynamics provides us with information of the coil. We call it Electro-Mechano-Optical (EMO) system. This EMO transition can be applied to a detection of nuclear magnetic resonance (NMR), which has been studied at Research Center for Advanced Science and Technology (RCAST) and Kyoto University.We are aiming at improving both mechanical and optical Qs of the EMO system to reduce the Brownian noise and thus to boost the SNR.
The manipulation of the optical spring complements its utility as a noiseless probe, which can be realized by state-of-the-art quantum filters. We will demonstrate proof-of-principle experiments in the next 3-4 years and achieve an outcome through the three selective applications of great scientific interest by the end of the research project.
Antoine Heidmann (Laboratoire Kastler Brossel)
Kentaro Somiya (Tokyo Institute of Technology)
Jerome Degallaix (Laboratoire des Matériaux Avancés)
Pierre Francois Cohadon (Laboratoire Kastler Brossel)
Yuta Michimura (University of Tokyo)
Koji Usami (Research Center for Advanced Science and Technology, UT)
Nobuyuki Matsumoto (Tohoku University)
Kazuyuki Takeda (Kyoto University)
Naoki Yamamoto (Keio University)
Masa-Katsu Fujimoto (NAOJ/Tokyo Institute of Technology)
Kentaro Komori (University of Tokyo)
Rion Shimazu (Keio University)