Students: Young-Shin Park Scott Lacey Mark Kuzyk Laser Cooling of an Optomechanical Microresonator Hailin Wang Oregon Center for Optics, University of Oregon Supported by NSF and DARPA

Introduction: What is optomechanics Optical control of mechanical motion Optomechanical resonator: Silica microsphere Optical and mechanical properties Toward ground state cooling: Combining cryogenic and laser cooling Summary and outlook Outline

Optomechanical Resonator Optomechanical coupling: Circulating optical power exerts a radiation pressure force on the mirror. The mirror displacement changes the cavity frequency,  0. Back Action:  0 in turn induces changes in the circulating optical power. For a review, see Kippenberg and Vahala, Science 321, 1172 (2008). LL mm 00 Support lifetime:  F F: Radiation pressure force:

Time Domain: Dynamical Backaction V.B. Braginsky, 1977; M. I. Dykman, LL mm 00 Support lifetime:  F  rad  > 0, damping  rad  < 0, amplification The delayed backaction leads to a radiation pressure force that depends on the velocity. Optical spring effects The induced change in the circulating optical power is delayed by the cavity lifetime.

Spectral Domain: Stokes and Anti-Stokes Processes Anti-Stokes process leads to cooling or damping. Stokes process leads to amplification. LL mm 00 Support F Scattering of photons from a mechanical vibration Photons LL 00 Anti-Stokes Cavity resonance LL 00 Stokes Cavity resonance

“ Putting the Mechanics Back in Quantum Mechanics ” Quantum behavior in a macroscopic mechanical system –Macroscopic superposition and entanglement –Decoherence –Quantum measurements –The quantum-classical boundary. Sensitive or precision measurements –Force, mass, etc. –Displacement Cooling of a macroscopic mechanical oscillator to its motional ground state. Schwab and Roukes, Physics Today, 58(7), 36 (2005).

Similar to parametric down conversion. SS mm LL LL SS 00 Stokes mm Quantum state transfer between optical and mechanical states.  AS mm LL Anti-Stokes LL  AS 00 mm Zhang et al., PRA 68, (2003); Genes et al., PRA 78, (2008). The quantum correlations become important at relatively low phonon occupation. The system is driven by a classical laser field at  L. a + and b + are creation operators for the cavity and the mechanical modes, respectively. Tool Box for Quantum Optics

Diedrich et al., Phys. Rev. Lett. 62, 403 (1989). Resolved sideband limit: Cooling the mechanical motion of an ion to its motional ground state. Photon  AS SS | g, N  1> | e, N  1> | e, N > | g, N > | g, N+1 > | e, N+1 > Phonon emission (gain) Phonon absorption (Cooling) Stokes Anti-Stokes Laser Cooling of Trapped Ions

Wilson-Rae et al., Phys. Rev. Lett. 99, (2007); Marquardt et al., Phys. Rev. Lett. 99, (2007).  AS SS | n, N  1> | n+1, N  1> | n+1, N > | n, N > | n, N+1 > | n=1, N+1 > LL  AS SS  Resolved sideband limit: Resolved-sideband cooling can in principle cool an optomechanical system to its motional ground state. Resolved-Sideband Optomechanical Cooling

Cohadon et al., Phys. Rev. Lett. 83, 3174 (1999). N ~ 170,000 Kleckner et al., Nature 444, 71 (2006). N ~ 220,000 Poggio et al., Phys. Rev. Lett. 99, (2007). N ~ 23,000 Gigan et al., Nature 444, 67 (2006). N ~ 740,000 Arcizet et al., Nature 444, 71 (2006). N ~ 260,000 Schliesser et al., Phys. Rev. Lett. 97, (2006). N ~ 3,900 Corbitt et al., Phys. Rev. Lett. 98, (2007). N ~ 10 8 Thompson et al., Nature 452, 72 (2008). N ~ 1,000 Schliesser et al., Nature Phys. 4, 415 (2008). N ~ 1,000 (Sideband cooling) Dynamical backaction cooling Active feedback cooling Ground state cooling Resolved-Sideband cooling + Cryogenic cooling Optomechanical Cooling at Room Temperature Cooling rateHeating rate

Frequency  m /  Mechanical Q Material Bath temperature Final phonon occupation 118 MHz 4.0 3,400 silica 1.4 K MHz 3.4 2,000 silica 1.65 K 63 ± MHz ,000 silicon nitride 5.3 K 32 MPQ/EPFL IQOQI/Cornell U. of Oregon Cryogenic cooling + Sideband Cooling 20  m Schliesser et al., Nature Phys. 5, 509 (2009). Park and Wang, Nature Phys. 5, 489 (2009). Groblacher et al., Nature Phys. 5, 485 (2009 ). Quantum correlations can already persist at this level of phonon occupations. Route to “the Ground State”

Optomechanical Crystals Eichenfield et al., Nature 462, 78 (2009). Applications in photonics: Sensing Optical routing and switching

Introduction: What is optomechanics Optical control of mechanical motion Optomechanical resonator: Silica microsphere Optical and mechanical properties Toward ground state cooling: Combining cryogenic and laser cooling Summary and outlook Outline

Q-factors as high as can be achieved. Extremely small absorption and scattering loss in high purity silica Nearly atomically smooth silica surface. Braginsky et al., Phys. Lett. 137, 393 (1989). Whispering gallery modes form via total internal reflections along the equator. CO 2 laser 30  Silica Microsphere

WGMs cannot be excited via geometric optical processes. Excite WGMs with evanescent waves via a tapered fiber Excite WGMs with evanescent waves via frustrated total internal reflection Launching WGMs via Evanescent Waves Difficult to implement at cryogenic temperature Cai et al., PRL 85, 74 (2000). Develop a new technique for direct free-space excitation of WGMs

Radius  =  critical angle Glancing incidence  Barrier The angle of incidence is no longer conserved in a deformed resonator.  Quantum analogy: The evanescent escape rate: depends on , increases exponentially as  approaches the critical angle. Evanescent Escape of WGMs

Strong evanescent escape occurs in these regions where the angle of incident reaches a minimum. sin  c sin     Evanescent Escape in a Deformed Resonator S. Lacey et al., Phys. Rev. Lett. 91, (2003).

Deformed Silica Microspheres Deformed micropheres are formed by fusing two regular microspheres of similar size with a CO 2 laser. Deformation is controlled by repeated heating. Deformation z x z y y x 20  m CO 2

Q-Factor and Emission Patterns vs Deformation Wavelength (nm) Q ~10 4 Q ~3x10 7 Q ~7x10 7  (degrees) Intensity (arbitrary units) Lacey et al., Phys. Rev. Lett. 91, (2003). 

Free space evanescent excitation of WGMs Launching WGMs in free-space by focusing a laser beam in areas 45 o from a symmetry axis. Approaching the sphere Park et al., Nano Lett. 6, 2075 (2006) Excitation efficiency as high as 50% can be achieved.

Silica Microsphere as Optomechanical Resonator Optical resonator : Whispering gallery modes Frequency ~ Hz Optical Q-factor ~ 10 8 Mode volume ~ 100  m 3 20  m Mechanical resonator: Breathing modes Frequency ~ 100 MHz Mechanical Q-factor ~ 10,000 Effective mass ~ 35 ng F rad

Optically Active Mechanical Modes D = 30  m Frequency (MHz) Noise Power Spectrum (dBm) (n, l )=(1,0) (n, l )=(1,2) Size dependence Finite element Analysis (n, l )=(1,2)(n, l )=(1,0)(n, l )=(1,4) (n, l ) = (radial, angular) Park and Wang, Opt. Express 15, (2007).

Optical Homodyne Detection of Mechanical Vibrations Local Oscillator E cav The breathing mechanical motion induces a phase shift in the circulating cavity field. Homodyne detection measures the induced phase shift. The oscillating phase shift leads to resonances at  m in the noise power spectrum of the homodyne measurement. Sensitivity!!!

Mechanical Quality Factor Mechanical loss of a silica microresonator Clamping loss due to the fiber stem Collisions by surrounding gases Acoustic attenuation (below room temp.) Mechanical quality factor (n, l )=(1,2) in vacuum Stem size: ~ 1/10 of microsphere diameter

Temperature Dependence of Mechanical Q-factor Dynamics of the dangling bonds leads to acoustic attenuation. Phillips, Amorphous Solids (1981). Pohl et al., Rev. Mod. Phys. 74, 991 (2002). Vacher et al., Phys. Rev. B 72, (2005). Thermally activation Tunneling ŸAcoustic attenuation in silica becomes important below room temperature Amorphous solid Mechanical damping due to acoustic attenuation remains significant at a few K.

Introduction: What is optomechanics Optical control of mechanical motion Optomechanical resonator: Silica microsphere Optical and mechanical properties Toward ground state cooling: Combining cryogenic and laser cooling Summary and outlook Outline

Experimental Setup Opto-mechanical cooling Cryogenic cooling He 4 cryostat The same laser beam is used for both radiation pressure cooling and homodyne detection.

T bath = 20K Normalized area Average phonon occupation Bath temperature (K) (n, l) = (1, 2) Equipartition Theorem Cryogenic Cooling

Resolved-sideband cooling at T bath =3.6 K P = 10 mW 40 mW 60 mW 83 mW Noise power spectrum ( m 2 /Hz) LL 00  /  = 23 MHz The spectrally-integrated area decreases with laser power. The linewidth of the mechanical resonance increases with laser power. Q m = 1600 (due to ultrasonic attenuation in silica at low temperature) D = 25.5  m (n, l) = (1, 2) T eff ~ 1 K

P in = 20 mW 60 mW 83 mW P th = 35 mW Radiation Pressure Cooling (No free parameters) P th : threshold power for parametric oscillation LL 00  /  = 23 MHz

Resolved-Sideband Cooling at T bath =1.4 K Quantum correlations can already persist at this level of phonon occupation. Limited by ultrasonic attenuation Q m = 3400 at 1.4 K (Q m = 10,300 at 300 K) LL 00  / 2  = 30 MHz D = 26.5  m, (n, l) = (1, 2) T eff ~ 210 mK N final ~ 37

Acoustic Attenuation at Low Temperature Silica Pohl et al., Rev. Mod. Phys. 74, 991 (2002). At ultrasonic frequency, acoustic attenuation decreases rapidly below T ~ 2 K and diminishes at T ~ 200 mK.

Combined resolved-sideband cooling with cryogenic cooling by using a silica optomechanical resonator. Demonstrated N final ~ 37 and T eff ~ 210 mK, limited by acoustic attention in silica. Future work Using a 3 He cryostat to lower the bath temperature and to minimize the acoustic attenuation. Using a crystalline optomechanical resonator. Pursuing quantum optics with optomechanical resonators. Summary

Cavity QED + Cavity Optomechanics Coupling a mechanical oscillator to a spin excitation. Park et al., Nano Lett. 6, 2075 (2006); Larsson et al., Nano Lett. 9, 1447 (2009). Nanocrystals  mm Nitrogen vacancy center in diamond

Electromechanical System A nanomechanical beam is capacitively coupled to a single electron transistor or to a superconducting microwave resonator. LaHaye et al., Science 304, 74 (2004); Teufel et al., Phys. Rev. Lett. 101, (2008) Nanomechanical beam : m ~ g;  /2  20 MHz Temperature < 50 mK (dilution refrigerator) Lowest thermal phonon occupation: N ~ 25

Mechanical Displacement: Calibration Schliesser et al., New J. of Phys. 10, (2008). Local Oscillator E cav Mimic the phase shift due to the mechanical vibration by phase-modulating the input optical field: Correspondence between r m and  : (  ) (with an E-O modulator)

Dependence on Laser Detuning Not sensitive ! Noise power spectrum (a.u.) Frequency (MHz) The sensitive of the direct homodyne detection depends on the laser detuning.  =  L   0 LL 00 WGM resonance Power spectrum at  m Laser detuning,  (MHz) Intensity The same laser beam can be used for both radiation pressure cooling and homodyne detection.

Blue shift Red shift Nonlinear Optical Properties at Low Temperature Regenerative pulsation at 18.5 K Park and Wang, Opt. Lett. 32, 3104 (2007).

St. Paul’s Cathedral, London Lord Rayleigh, Echo Wall of the Temple of Heaven, Beijing, Ming dynasty, 1420 Whispering Gallery Acoustic Waves