Young-Shin Park and Hailin Wang Dept. of Physics and Oregon Center for Optics, Univ. of Oregon CLEO/IQEC, June 5, Supported by NSF and ARL

Transcription

1 Resolved--sideband cooling of an optomechanical Resolved resonator in a cryogenic environment Young-Shin Park and Hailin Wang Dept. of Physics and Oregon Center for Optics, Univ. of Oregon CLEO/IQEC, June 5, 2009 Supported by NSF and ARL

2 Outline Introduction Optomechanical microsphere resonator Free-space excitation of WGMs Homodyne detection of mechanical displacement Mechanical damping Resolved sideband cooling at cryogenic temperature Summary

3 Laser cooling of atoms Doppler cooling Photon k vi A L A vf vi spontaneous emission Radiation pressure force acts as a velocity dependent viscous force. F v Radiation pressure cooling of Mg ions, Wineland et al., PRL (1978). Laser deceleration of Na atoms, Phillips et al., PRL (1982). Optical molasses, Chu et al., PRL (1982). Below the Doppler limit (~43µK, Na atoms), Lett et al., PRL (1988). Below the one photon recoil (~2µK, 4He atoms), Aspect et al., PRL (1988).

4 Sideband cooling of a trapped ion vib Photon vib e,n e,n 1 L 0 vib e,n 1 vib L 0 AS S g,n 1 g,n g,n 1 A single Hg ion in the ground state of its confining well, ~95% of the time. Diedrich et al., Phys. Rev. Lett. 62, 404 (1989).

5 Putting the mechanics back in quantum mechanics Cool the macroscopic oscillator to the quantum mechanical ground state: E N th m N th 1 1 m kbt 2 e 1 Quantum mechanics in a macroscopic object: Quantum state of large ensemble (>1010 atoms) Macroscopic superposition and entanglement Quantum and classical boundary Ultrahigh sensitivity measurement in force and displacement Schwab and Roukes, Physics Today, 58(7), 36 (2005). Braginsky, et al., Quantum Measurement (1992). Marshall, et al., Phys. Rev. Lett. 91, (2003). Vitali, et al., Phys. Rev. Lett. 98, (2007).

6 Nanoelectromechanical resonator Cryogenically cooled nanoelectromechanical resonator. LaHaye et al., Science 304, 74 (2004).

7 Optomechanical resonator Effects of radiation pressure 0 Frad x Mechanical displacement Change in optical resonance m Delayed radiation pressure force due to finite cavity lifetime FRad x(t ) FRad ( x) Optical intracavity power Dynamical backaction leads to optomechanical cooling or gain For reviews, see for example Braginsky et al., Quantum Measurement (1992). Kippenberg and Vahala, Science 321, 1172 (2008). Marquardt and Girvin, Physics 2, 40 (2009). dfrad x dx

8 Dynamical backaction Finite cavity lifetime Force Displacement diagram Delayed Radiation L 0 0 pressure force Frad Laser Frad 0 Wnet Frad dx 0 Pcav x0 x0 x0 x0 L 0 frequency mirror s mechanical energy is lowered. Dynamical backaction leads optomechanical cooling (red-detuning) or heating (blue-detuning).

9 Equipartition theorem m m m Effective damping rate eff m opto mech Cooling eff The amplitude of thermal mechanical vibration is a measure of the temperature. Cooling of mechanical vibration results Teff meff meff in the area reduction (or linewidth widening) of displacement spectrum. kb kb x2 2 2 x ( ) d m Tbath 2 eff Displacement spectrum x 2 ( ) 4k B T meff ( 2 eff2 ) 2 eff2 2 Assuming no other heating.

10 Dynamical backaction cooling Dynamical backaction cooling Gigan et al., Nature 444, 67 (2006): ~10K (N~740,000) Arcizet et al., Nature 444, 71 (2006): ~ 10K (N~260,000) Schliesser et al., Phys. Rev. Lett. 97, (2006): ~11K (N~3,900) Corbitt et al., Phys. Rev. Lett. 98, (2007): ~ 0.8K (N~108) Thompson et al., Nature 452, 72 (2008): ~ 6.82mK (N~1,000) Active feedback cooling Cohadon et al., Phys. Rev. Lett. 83, 3174 (1999): ~15K (170,000) Kleckner et al., Nature 444, 71 (2006): ~ 135mK (N~220,000) Poggio et al., Phys. Rev. Lett. 99, (2007): ~2.9mK (N~23,000)

11 Resolved--sideband cooling Resolved m L L AS S AS S N 4 m L 0 m 2 N << 1 16 m2 >> 1 e,n 1 m e,n 1 L Stokes process is well suppressed in the 0 AS Anti-Stokes (Stokes) process decreases (increases) the phonon occupation by one. e,n m m resolved-sideband limit. S g,n 1 g,n g,n 1 cavity, phonon Wilson-Rae et al., Phys. Rev. Lett. 99, (2007). Marquardt et al., Phys. Rev. Lett. 99, (2007).

12 Why not using a (cryogenic) refrigerator? Technically refrigerator operating near quantum ground state temperature is not available. 100 MHz oscillator T (N=1) ~ 5mK Yes!! : Bath temperature can be lowered with current cryogenic technique. Optomechanical cooling Cryogenic cooling Difficulty : Carrying out the optomechanical cooling in a cryogenic environment.

13 Experimental challenges Goal Mechanical dissipation Quantum backaction Cryogenic operation Resolved sideband limit ( m ) Experimentally, need to overcome any heating from environment, such as laser noise, laser absorption. Wilson-Rae et al., Phys. Rev. Lett. 99, (2007). Marquardt et al., Phys. Rev. Lett. 99, (2007).

14 Route to the ground Cryogenic cooling + Sideband Cooling 20 µm MPQ/EPFL Frequency Sideband limit Mechanical Q (material) Bath temperature Final occupation 65.2 MHz 3.4 2,000 (silica) 1.65 K 63 ± 20 IQOQI 0.95 MHz ,000 (silicon nitride) 5.3 K 32 U. of Oregon 118 MHz 4.0 3,400 (silica) 1.4 K 37 Approaching the quantum ground state!! Schliesser et al., Nature Phys. to be published. Groblacher et al., Nature Phys. to be published. Park and Wang, Nature Phys. to be published.

15 Outline Introduction Optomechanical microsphere resonator Free-space excitation of WGMs Homodyne detection of mechanical displacement Mechanical damping Resolved sideband cooling at cryogenic temperature Summary

16 Optomechanical microsphere resonator Frad WGMs n = 1 (air) n = µm C sin 1 (1 n) Optical resonator : Mechanical resonator (R=15 µm): Whispering gallery modes Radial breathing modes Frequency ~ 1014 Hz Frequency > 100 MHz Optical Q-factor ~ 109 Mechanical Q-factor > 10,000 Mode volume ~ 200 µm3 Effective mass ~ 35 ng

17 Excitation of WGMs Frustrated total internal reflection Tapered fiber ( > 99%, critical coupling) gap ~ m 20 µm Cai et al., Phys. Rev. Lett. 85, 74 (2000). Need to control the gap with nanometer precision. Technically difficult in a cryogenic environment Microtoroid, Kippenberg

18 Deformed silica microspheres Fabrication 20 m z z x y a b y x 4.7% Deformation a b b 13.4% Deformed micropheres are formed by fusing two regular microspheres of similar size with a CO2 laser. Deformation is controlled by repeated heating. 2.4%

19 Directional emission 4.4% 2.4% Highly directional emission along with high Q-factors. Lacey et al., Phys. Rev. Lett. 91, (2003).

20 Evanescent escape The angle of incidence is conserved in a regular sphere. V eff Wave equation of WGMs 2 E n2k 2 E 0 2 E k 2 (1 n 2 ) E k 2 E Quantum mechanical analogy, = C: critical angle Veff l (l 1) 2 k (1 n2 ) 2 r 1 for r R n 0 for r R Glancing incidence Barrier R Radius

21 Evanescent escape The angle of incidence is no longer conserved in a deformed sphere. V eff Wave equation of WGMs 2 E n2k 2 E 0 2 E k 2 (1 n 2 ) E k 2 E Quantum mechanical analogy, = C: critical angle Veff l (l 1) 2 k (1 n2 ) 2 r 1 for r R n 0 for r R Glancing incidence Barrier R Radius The tunneling escape rate increases exponentially as the incident angle ( ) approaches the critical angle ( C).

22 Free space evanescent excitation of WGMs Launching WGMs in free-space by focusing a laser beam in areas 45 o m m m Fractional dip (%) Transmission from a symmetry axis. Data - Gauss fit Focused beam size ~ 1.8 µm / 2 83 MHz Detuning(GHz) Distance ( m) 1 2

23 Free space evanescent excitation of WGMs Launching WGMs in free-space by focusing a laser beam in areas 45 o enables : Free-space evanescent excitation 0.2 m 0.8 Low temperature 0operation.2 m mof mechanical displacement Homodyne detection Fractional dip (%) Transmission from a symmetry axis Data - Gauss fit Focused beam size ~ 1.8 µm / 2 83 MHz Detuning(GHz) Distance ( m) 1 2

24 Outline Introduction Optomechanical microsphere resonator Free-space excitation of WGMs Homodyne detection of mechanical displacement Mechanical damping Resolved sideband cooling at cryogenic temperature Summary

25 Direct homodyne detection Ecav Ecoupled Ein Eout Eout itecav ELO local oscillator The electric field coupled into the microsphere resonator experiences a phase shift due to the mechanical vibrations ( m). it Ein r E cav (t ) i ( 0 0 sin mt ) Ecav (t ) R Trt 2 : mode-matching coefficient T : transmittance : cavity decay rate r0 : radial amplitude η :coupling efficiency Hadjar et al., Euro. Lett. 47, 545 (1999).

26 Detuning dependence WGM resonance -200 / 2 54 MHz Noise spectrum (a.u.) (a.u.) Transmission spectrum Intensity Transmission spectrum Noiseamplitude amplitude (a.u.) (a.u.) Circle : data Line : calculation 148 MHz 0 Not sensitive! 148 MHz 200 Detuning (MHz)(MHz) Laser detuning, Frequency (MHz) Mechanical frequency (MHz)

27 Detuning dependence WGM resonance -200 / 2 54 MHz at =± m in the sideband limit, 148 MHz 0 Not sensitive! 148 MHz Detuning (MHz)(MHz) Laser detuning, Displacement sensitivity Noise spectrum (a.u.) (a.u.) Transmission spectrum Intensity Transmission spectrum Noiseamplitude amplitude (a.u.) (a.u.) Circle : data Line : calculation rmin Frequency (MHz) Mechanical frequency (MHz) 2 0 R m ~ m / Hz m Pin 0.03, Pin 1 mw

28 Optically observable mechanical modes Finite element Analysis (n, l )=(1,2) (n, l )=(1,0) (n, l )=(1,4) -40 Mode numbers (n, l) = (radial, angular) D = 30 m Frequency (MHz) Mechanical frequency (MHz) Transmission spectrum (dbm) Size dependence of vibration modes 200 (n, l )=(1,0) 150 (n, l )=(1,2) Lines : theory Dots : experimental data Diameter ( m) Park and Wang, Opt. Express 15, (2007).

29 Effective mass : Calculation Effective mass coefficient (α ) Finite element Analysis (n, l )=(1,2) (n, l )=(1,0) (n, l )=(1,4) effective mass (meff ) microsphere mass (m) 2 Em m A m 1.14 Displacement power spectrum x 2 ( ) m 4k B T meff ( 2 eff2 ) 2 eff Equipartition theorem x2 k BT meff m2

30 Mechanical Displacement: Calibration The input field is phase-modulated at frequency with a depth in order to mimic the phase shift due to mechanical vibration1). Ecoupled Optic i sin t Ein Electro E e in Modulator Ecav Eout Eun-coupled Noise spectrum (10-32m2/Hz) 100 / MHz 10 Modulation depth for same signal 0 r0 m R m / MHz αsimulation (= 1.14) αmeasured (= 1.16 ± 0.03) Frequency (MHz) For (n, l ) = (1,2) mode 1) Schliesser et al., New J. of Phys. 10, (2008).

31 Outline Introduction Optomechanical microsphere resonator Free-space excitation of WGMs Homodyne detection of mechanical displacement Mechanical damping Resolved sideband cooling at cryogenic temperature Summary

32 Mechanical loss Mechanical quality factor Mechanical loss of a silica micro-resonator m Qm m Acoustic absorption (low temp.) m i Clamping loss (room temp.) Loss due to collisions with surrounding gases Noise power spectrum (10-33 m2/hz) Thermoelastic loss (negligible) 6 (n, l )=(1,2) Qm 18, 000 in vacuum Stem size: ~ 1/10 of microsphere diameter Frequency (MHz) 99.26

33 Ultrasonic attenuation in silica Mechanical linewidth (khz) Phonon interaction in twolevel tunneling defects Thermally activated relaxation process Qm m / MHz 150 Si O 100 Ultrasonic attenuation in amorphous solids due to 50 0 Qm 3,400 1 redistribution of asymmetric Qm 10,000 double-well potentials on strained Si-O-Si bonds with Temperature (K) changing temperature. Loss due to ultrasonic attenuation in silica microsphere is important below room temperature. Phillips, Amorphous Solids (1981). Pohl et al., Rev. Mod. Phys. 74, 991 (2002). Vacher et al., Phys. Rev. B 72, (2005).

34 WGM resonance shift (GHz) Optical properties at low temperature 1.5 Blue shift Red shift Temperature (K) 25 d 1 dr 1 dn 0 ( ) dt R dt n dt Thermal effects are reduced at low temperature. Regenerative pulsation at 18.5 K Park and Wang, Opt. Lett. 32, 3104 (2007).

35 Outline Introduction Optomechanical microsphere resonator Free-space excitation of WGMs Homodyne detection of mechanical displacement Mechanical damping Resolved sideband cooling at cryogenic temperature Summary

36 1/2 m / 2 1 Qm 11, 200 Tbath 300 K MHz Red detuning Noise spectrum (10 m/hz ) Resolved--sideband cooling at room temperature Resolved / 2 38 MHz Teff 11 K 0.1 = 2 (10 khz+260 khz) Teff = (γeff / γm) Tbath ~ 11K < N >final ~ 2,000 >> 1 Assuming no other heating Frequency (MHz) (n, l ) (1, 2) mode Input power (mw) 50 Effective temperature (K) eff m Effective linewidth (khz) 115.4

37 Experimental setup for cryogenic operation Via Free space excitation Cryogenic cooling Opto-mechanical cooling He4 cryostat Tbath ~ 1.4K Objective lens 3-D stage

38 Noise spectrum Cryogenic Cooling m / 2 113MHz Bathtemperature temperature (K) Bath (K) Average occupation phonon occupation Average phonon Noise spectrum area Displacement spectrum area(a.u.) (a.u.) Frequency m / MHz Temperature (K) Mechanical mode temperature is in equilibrium with bath temperature Mechanical frequency (MHz) Mechanical linewidth (khz) Tbath = 20K

39 m mw 60 mw 83 mw Pin = 10 mw Linewidth (khz) Tbath = 3.6 K Integrated area Noise spectrum Displacement m2/hz) /Hz) spectrum(10 (10-36m Resolved--sideband cooling at Tbath=3.6 K Resolved Frequency (MHz) Γ/2π = 200 khz γm /2π =80 khz Pump power (mw) 10 Pump power (mw) Area reduction m / MHz / 2 23 MHz Teff ~ 1.0 K Linewidth widening Cooling ratio ~ 3.5 Incident laser induces negligible heating. Limited by ultrasonic attenuation Qm = 1,600 10,000 (room T)

40 Resolved--sideband cooling at Tbath=3.6 K Resolved Lines : theory, Dots : data eff (khz) 300 m / MHz Tbath = 3.6 K / 2 23 MHz m / 2 80 khz 200 Radiation pressure cooling is dominant. Frequency shift (khz) (No other free parameters) m / MHz m2 P m Pth 4( ) 2 2 [ Pin = 20 mw 60 mw 83 mw Pth = 35 mw -1.0 Laser detuning ( / m) ] 2 2 4( m ) 4( m ) m2 P m Pth 4( ) [ m m ] 4( m ) 2 2 4( m ) 2 2 Pth : parametric oscillation threshold power.

41 Ultrasonic attenuation at lower temperature Silica Ultrasonic attenuation decreases rapidly below ~ 5K for ultrasonic frequencies. Pohl et al., Rev. Mod. Phys. 74, 991 (2002).

42 Resolved--sideband cooling at Tbath=1.4 K Resolved Tbath = 1.4 K Integrated area 246 eff (khz) / khz m / 2 35 khz Pump power (mw) Pump power (mw) 25 Average phonon occupation 1 m / MHz / 2 30 MHz Area reduction Linewidth widening Teff ~ 210mK. <N>final ~ 37. Incident laser induces negligible heating. Limited by ultrasonic attenuation Qm = 3,400 10,300 (room T)

43 Cooling of nanomechanical resonator For comparison : Nanomechanical resonators in a sub-kelvin cryogenic temperature. <N>final ~ 25 : cryogenically cooled nanomechanical resonator. Naik et al., Nature, 443, 193 (2006). <N>final ~ 140 : Dynamical backaction cooling is limited by radiation heating. Teufel et al., Phys. Rev. Lett. 101, (2008).

44 Summary and Future work Summary Demonstrated the resolved sideband cooling of a silica microsphere resonator in a cryogenic environment by utilizing free space excitation of WGMs. Achieved average phonon occupation, <N> ~ 37, for a 110MHz mechanical oscillator, limited by acoustic absorption. Future work Carry out experimental studies in a He3 cryostat in order to lower both bath temperature and acoustic absorption.

45 Future work Combining cavity-qed with cavity optomechanics: e.g. Coupling a mechanical oscillation to a spin excitation. Frad 0 Nanocrystals m Park et al., Nano Lett. 6, 2075 (2006). Thank you for your attention!