opto-mechanical filtering

Transcription

1 opto-mechanical filtering Robert L. Ward Australian National University Gravitational Wave Advanced Detector Workshop Waikoloa, HI, 22

2 squeezing accomplished now that we ve got the ellipse we need, let s rotate it 2

3 workshop This is a workshop presentation. I m hoping you will understand what I m trying to say, so you can explain it to me later today by the pool. 3

4 ponderomotive--optical rigidity the radiation pressure on a moveable mirror converts amplitude modulation into phase modulation. this coupling of the quadratures can be used to generate squeezing. 5 Thomas Corbitt, Yanbei Chen, Farid Khalili, David Ottaway, Sergey Vyatchanin, Stan Whitcomb, and Nergis Mavalvala. Squeezed-state source using radiation-pressure-induced rigidity. PDH Response for Detuned Cavity the dispersion resulting from the optical rigidity can also be used to filter an already-squeezed input field. ponderomotive squeezing recently reported D. W. C. Brooks, T. Botter, N. Brahms, T. P. Purdy, S. Schreppler, and D. M. Stamper-Kurn. Ponderomotive light squeezing with atomic cavity optomechanics. ArXiv e-prints, July 2. 4 mag phase [deg] On resonance nm

5 opto-mechanically induced transparency pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi using the ponderomotive effect, OMIT is an optomechanical C analogue of electromagnetically induced transparency Probe Control Control field Probe field x(t) Probe in Probe out r probe = +if( ) i( + ) + apple/2 + 2 f( ) capple t r 2 Probe frequency f( ) = ~G 2 ā 2 ( ) i( ) + apple/2 ( ) = m eff 2 m 2 i m 5 Stefan Weis, Rémi Rivière, Samuel Deléglise, Emanuel Gavartin, Olivier Arcizet, Albert Schliesser, and Tobias J. Kippenberg. Optomechanically induced transparency. Science, 33(6): , 2. OMIT and ponderomotive squeezing are kind of the same thing Thierry Botter, Daniel W. C. Brooks, Nathan Brahms, Sydney Schreppler, and Dan M. Stamper-Kurn. Linear amplifier model for optomechanical systems. Phys. Rev. A, 85:382, Jan 22.

6 cavity reflection Reflected Probe Power =! c phase [rad] (ω p ω c ) [Hz] x 5 =! c cavity linewidth apple = khz 6

7 make the back mirror moveable Reflected Probe Power =! c! m = m apple phase [rad]! c (ω p ω c ) [Hz] x 5 7 = The mirror motion is driven by the beat between the control and probe beams. This motion upconverts control laser light, where it can interfere with the probe beam.

8 look closer Reflected Probe Power phase [rad] OMIT = m + 2 c/apple c =2Gāx zpf (ω p ω c ) [Hz] x 5 Reflected Probe Power phase [rad] ! c (ω p ω c ) [Hz] =! c! m = = Resonance width depends on mechanical resonance, and optomechanical cooperativity (which depends on optomechanical coupling and in-cavity amplitude).

9 over-coupled cavity Reflected Probe Power =! c! m = phase [rad] (ω p ω c ) [Hz] Strongly overcouple the cavity. Still get the phase shift. Looks like a great filter cavity. 9 =! c

10 parameters desired width: OMIT = m + 2 c/apple Hz cavity linewidth apple khz mech. frequency! m MHz mech. Q Q m 6 optomechanical coupling c =2Gāx zpf 2 khz A system with ~these parameters can be realised with commercially available components.

11 , B. M. Zwickl, A. M. Jayich, Florian Marquardt2, S. M. Girvin,3 & J. G. E. Harris,3 a high finesse system: membrane in the middle anical objects and electromagnetic degrees of e to each other through radiation pressure. stems in which this coupling is sufficiently d to show quantum effects and are a topic of st. Devices in this regime would offer new types quantum state of both light and matter 4, and ew arena in which to explore the boundary nd classical physics5 7. Experiments so far have optomechanical coupling to laser-cool mechut have not yet reached the quantum regime. chnical challenge in this field is integrating hanical elements (which must be small, light igh-finesse cavities (which are typically rigid out compromising the mechanical or optical. A second, and more fundamental, challenge e mechanical element s energy eigenstate. surements (no matter how sensitive) cannot ator s energy eigenstate3, and measurements ies other than displacement4 6 have been difpractice. Here we present an optomechanical potential to resolve both of these challenges. cavity which is detuned by the motion of a 5membrane placed between two macroscopic, mirrors. This approach segregates optical and nality to physically distinct structures and ng either. It also allows for direct measurement membrane s displacement, and thus in prin s energy eigenstate. We estimate that it should m this scheme to observe quantum jumps of a6 m an important goal in the field of quantum x c e High Q, resonant frequency (fundamental mode ~ 3kHz for mm x mm x 5 nm). Q =! m theoretical proposals aiming to study quantum action between optical cavities and mechanical on cavities in which one of the cavity s mirrors is L d AOM Use a SiN membrane as mechanical oscillator. Cheaply available. x!l!p DAQ Laser b PI 4 rc =. rc = ωcav/ωfsr a rc =.88 rc =.6 rc =.3 2 rc =..5 x/λ J. D. Thompson, B. M. Zwickl, A. M. Jayich, Florian Marquardt, S. M. Girvin, and J. G. E. Harris. Figure Schematic of the dispersive optomechanical set-up. Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane. Nature, a, Conceptual illustration of reflective optomechanical coupling. The cavity 452(783):72 75, mode (green) is defined by reflective surfaces, one of which is free to move. The cavity detuning is proportional to the displacement x. b, Conceptual illustration of the dispersive optomechanical coupling used in this work.

12 concept beam combiner/ separator cavity apple =! m Control field filter cavity Probe field externally generated squeezed vacuum field 2

13 challenges Optical losses membrane has complex index of refraction; imaginary part ~ -4 impact depends on microscopic position (and thus opto-mechanical coupling) Modal overlap membrane acoustic mode not perfectly matched to optical mode membrane higher order modes Thermal noise some form of cooling necessary combination of refrigeration and laser cooling (resolved sideband) more on this from Zach coming up next! B. M. Zwickl, et al. Applied Physics Letters, 92():325, 28. y (µ m) z (µ m) Yi Zhao, et al. Opt. Express, 2(4): , Feb 22. 3

14 laser cooling the membrane can theoretically be cooled to the quantum ground state T eff = T m m + OM OM =4G 2 x 2 zpfā/apple /2π (khz) a MHz ( sl m )/2π (MHz), n c Norm. reflection b n PSD (m 2 Hz ) 3 PSD (m 2 Hz ) n = ( m )/2π (khz) 35 n =.85 ( m )/2π (MHz)., n c c d e recall: c =2Gāx zpf laser cooling changes the OMIT linewidth, so cannot rely on it too much Figure 4 Optical cooling results. a, Measured mechanical mode linewidth damping alone. Error bars ind Jasper Chan, T. P. Mayer Alegre, Amir H. Safavi-Naeini, Jeff T. Hill, Alex (squares), EIT transparency bandwidth (circles) and predicted optomechanical Supplementary Information. c damping rate estimated Krause, usingsimon the zero-point Groblacher, optomechanical Markus Aspelmeyer, coupling rate, and Oskar laser intracavity Painter. photon numb g/2p 5 9 khz (redlaser dashedcooling line). Inset, of a measured nanomechanical EIT transparency oscillator window into its at quantum mechanical ground damping rate vers the highest cooling-beam state. drive Nature, power. 478(7367):89 92, b, Measured (circles) 2. average phonon damping dependence on n c is number, n, in the breathing mechanical mode at v m /2p GHz, versus Supplementary Information. e cooling drive-laser power (in units of intracavity photons, n c ), as deduced from versus drive-laser power (n c ), the calibrated area under the Lorentzian line shape of the mechanical noise dashed curve corresponds to t power spectrum. The inset spectra show the measured noise PSD (using limited detection but all other x zpf fm, corresponding to the numerically computed motional mass for experiment. The solid black cu the breathing mode with m 5 3 fg). The dashed blue line indicates the position measurement of mec estimated mode phonon number calculated from the measured optical 4 2 Macmillan Publishers Limited. All rights reserved 6 O C

15 electro-opto-mechanical engineer non-uniform capacitor plates around the membrane. Fringing fields creative capacitive sensor/actuator, like ESD in aligo. Couple mechanical system to electronic oscillator --> modify mechanical susceptibility. Use an electronic oscillator rather than mechanical oscillator. thermal noise? Capacitive coupler never been done requires ~ um size electrode gap other actuator/sensor systems possible (e.g., second laser) J. M. Taylor, A. S. Sørensen, C. M. Marcus, and E. S. Polzik. Laser cooling and optical detection of excitations in a lc electrical circuit. Phys. Rev. Lett., 7:2736, Dec 2. 5

16 and someone s already built something like it A fiber-coupled system on a chip, with a Si disk resonator evanescently coupled to a SiN ring, with electronic actuation. Batch processible. Oscillator f, Q, too low, and fibers are lossy. H. Miao, K. Srinivasan, and V. Aksyuk. A microelectromechanically controlled cavity optomechanical sensing system. ArXiv e-prints, April 22. 6

17 Control field Probe field 7