UA Math 2010 Cavity optomechanics … From the top down: Review of optomechanical mirror cooling Coupling to ultracold atoms and molecules From the bottom up: Bosonic & fermionic atomic mirrors Outlook: All-optical optomechanics ARONSFONR Mishkat Bhattacharya (  U. Rochester) Wenzhou Chen Dan Goldbaum Rina Kanamoto (  Ochanomizu University) Greg Phelps Swati Singh Ewan Wright Key Zhang (  Shanghai)

UA Math 2010 quantum metrology How can quantum resources be exploited with maximal robustness and minimal technical overhead? What are the inherent sensitivity-reliability tradeoffs in quantum sensors? What is the role of particle statistics in quantum metrology? How do decoherence mechanisms set fundamental limits to measurement precision? This talk: From the top down: Cooled nanoscale cantilevers for sensing and quantum control of AMO systems From the bottom up: optomechanics in quantum-degenerate atomic systems

UA Math 2010 From the top down…

UA Math 2010 micromechanical cantilevers – single-particle detectors Protein detection Three cantilevers coated with antibodies to PSA, a prostate cancer marker found in the blood. The left cantilever bends as the protein PSA binds to the antibody. Photo courtesy of Kenneth Hsu/UC Berkeley & the Protein Data Bank Micromechanical cantilever with a single E. Coli cell A micromechanical cantilever with a single E. Coli cell attached. The cantilever is used to detect changes in mass due to selectively attached biological agents present in small quantities. Craighead Research Group, Cornell University

UA Math 2010 micro-mirrors D. Kleckner & D. Bouwmeester, Nature 444, 75 (2006) SEM photograph of a vertical thermal actuator with integrated micromirror. Application of a current to the actuator arm produces vertical motion of the mirror, which can either reflect an optical beam or allow it to be transmitted. (Southwest Research Institute,

UA Math 2010 Optical spring effect: - laser radiation increases - Requires cavity tuned below laser frequency Optical damping: - Requires cavity tuned above laser frequency Use two lasers! radiation pressure mirror cooling Basic idea: change frequency and damping of a mirror mounted on a spring using radiation pressure Number of quanta of vibrational motion: [ H. Metzger and K. Karrai, Nature 432, 1002 (2004) ] [ T. Corbitt et al, PRL 98, (2007) ]

UA Math 2010 optical spring effect Goal: increasing Trapping due to `optical spring’: B. S. Sheard et al. PRA 69, (R) (2004) Need red-detuned cavity

UA Math 2010 optical damping Goal: decreasing Cooling due to asymmetric pumping of sidebands (resolved sidebands limit) M. Lucamarini et al., PRA 74, (2006) A. Schliesser et al. PRL 97, (2006) Need blue-detuned cavity

UA Math 2010 Adiabatic and non-adiabatic (optical delay) contributions: Adiabatic effect – “optical spring” (also bistability and multistability) Non-adiabatic effect a simple theory Linear coupling:, integrate equation for a formally, keeping terms up to

UA Math 2010 prehistory V. Braginsky, “Measurement of Weak Forces in Physics Experiments” (Univ. of Chicago Press, Chicago, 1977). V.B. Braginsky and F.Y. Khalili, "Quantum Measurement'' (Cambridge University Press, Cambridge, 1992) C. M. Caves, Phys. Rev. D23, 1693 (1981). A. Dorsel, J. D. McCullen, PM, E. Vignes and H. Walther,” Optical bistability and mirror confinement induced by radiation pressure,” PRL 51, 1550 (1983).

UA Math 2010 early history 18K Cavity cooling of a microlever, C. Höhberger-Metzger & K. Karrai, Nature 432, 1002 (2004)

UA Math 2010 S. Gigan et al. (Zeilinger group) “Self-cooling of a micromirror by radiation pressure”, Nature 444, 67 (2006) O. Arcizet et al. (Pinard/Heidman group) “Radiation pressure cooling and optomechanical instability of a micromirror”, Nature 444, 71 (2006) D. Kleckner et al. (Bouwmeester group) “Sub-Kelvin optical cooling of a micromechanical resonator”, Nature 444, 75 (2006) A. Schliesser et al. (Vahala/Kippenberg groups) “Radiation pressure cooling of a micromechanical oscillator using dynamical back-action” PRL 97, (2006) T. Corbitt et al. (LIGO) “An all-optical trap for a gram-scale mirror”, PRL 98, (2007), “Optical dilution and feedback cooling of a gram-scale oscillator”, PRL 99, (2007) A. Vinante et al (AURIGA gravitational wave detector mirror), M eff = 1,100 Kg, PRL 101, (2008) recent history < 10K 10K 135 mK 11K 0.17 mK 6.9 mK

UA Math 2010 hot off the press… (17 March 2010)

UA Math 2010 a broad range of systems From T. Kippenberg and K. Vahala Science 321, 1172 (2008) (CPW: coplanar plane wave)

UA Math 2010 cantilevers for quantum detection and control Pushing quantum mechanics to truly macroscopic systems Quantum superpositions and entanglement in macroscopic systems Novel detectors Coherent control Single-domain ferromagnet with oscillatory component B(t) couples to atomic spin F Described by Tavis-Cummings Hamiltonian [P. Treutlein et al., PRL 99, (2007)] Recent experimental results: Treutlein et al., coupling via Casimir-Polder force

UA Math 2010 cantilever coupling to dipolar molecules

UA Math 2010 single dipolar molecule Electric dipoles Magnetic dipoles Used in Magnetic Force Microscopy Frequency shiftsqueezing

UA Math 2010 motional squeezing Classical cantilever motion, S. Singh, M. Bhattacharya, O. Dutta, PM, PRL101, (2008)

UA Math 2010 … and from the bottom up…

UA Math 2010 cavity optomechanics with atoms Single atomJ. Kimble, G. Rempe, … Utracold thermal gasD. Stamper-Kurn, Nature Phys. 4, 561 (2008) BECT. Esslinger, Science 322, 235 (2008) FermionsR. Kanamoto & PM, PRL 104, (2010) (theory) (also: Interferometers, quantum simulators,, clocks,…) Moving mirror  mechanical center-of-mass motion of atom(s)

UA Math 2010 cantilever coupling to Bose condensates lightmirrorrad. pressurecondensate-light interaction Condensate recoil: rad. pressure on BEC “mirror” T. Esslinger et al, Science 322, 235 (2008) D. Stamper-Kurn et al, Nature Physics 4, 56 (2008)

UA Math 2010 optomechanical coupling Classical dynamics, adiabatic elimination of optical field: Effective mirror:

UA Math 2010 potential

UA Math 2010 quasi-periodic orbits K. Zhang, W. Chen, M. Bhattacharya and PM, PRA 81, (2010)

UA Math 2010 chaotic orbits Next: quantum dynamics, entanglement quantum control quantum chaos (?) …

UA Math 2010 ring resonator system Let 2 Counter-propagating running waves

UA Math 2010 three-mode system Analog of 2 coupled optomechanical mirrors (W. Chen, D. S. Goldbaum, M. Bhattacharya and PM, arXiv: )

UA Math 2010 classical dynamics Dark states!

UA Math 2010 steady state intensity and phase Spontaneous symmetry breaking Symmetric pumping

UA Math 2010 steady state “positions” Spontaneous Symmetry breaking

UA Math 2010 Outlook – toward all-optical optomechanics optical tweezers fixed FP mirror Main advantage: Optical spring is coupled to reservoir at T~ 0 (S. Singh, D. Goldbaum, E. M. Wright, PM, in preparation)

UA Math 2010 effects of laser linewidth laser spectrum (G. Phelps)

UA Math 2010

nano-MRI Cantilever force sensor at the heart of IBM's"nano-MRI" microscope. IBM scientists have used this nano-MRI to visualize structures at resolution 60,000 times better than current magnetic resonance imaging technology allows. This technique brings MRI capability to the nanoscale level for the first time and represents a major milestone in the quest to build a microscope that could "see" individual atoms in three dimensions. With further development, applications could include understanding how individual proteins interact with drugs for discovery and development, and analyzing computer circuits only a few atoms wide.

UA Math 2010 two-wavelengths approach T. Corbitt et al, PRL 98, (2007) Spring constant damping k>0  >0 Dynamically unstable k>0  <0 Stable k<0  >0 “anti-stable” k<0  <0 Statically unstable (carrier) (subcarrier)

UA Math 2010 basic optomechanics − quantum approach But: So:

UA Math 2010 three-mirror geometry [ A. Dorsel et al., PRL 51, 1550 (1983); PM et al, JOSA B11, 1830 (1985); J. D. McCullen et al., Optics Lett. 9, 193 (1984) ]

UA Math 2010 three-mirror cavity See also: M. Bhattacharya and PM, PRL 99, (2007) M. Bhattacharya et al, PRA 77, (2008) Early discussion: PM et al., JOSA B2, 1830 (1985) … Nature 452, 72 (2008)

UA Math 2010 three-mirror cavity, R=1

UA Math 2010 three-mirror cavity, R<1 W. J. Fader, IEEE J. Quant. Electron. 21, 1838 (1985) 0 frequency

UA Math 2010 three-mirror cavity, R<1 allows preparation of energy eigenstates & observation of quantum jumps 0 frequency

UA Math 2010 a flavor of the full theory (R=1) Quantum Langevin equations of motion, input-output formalism: Noise operators:

UA Math 2010 experimental signatures

UA Math 2010 future ring cavity work Small quantum fluctuations Feeble quantized fields Revisit the Fabry-Pérot case Damping of the matter-wave side modes  Heating and cooling mechanisms Optical monitoring of matter-wave fluctuations via dark states

UA Math 2010 asymmetric pumping

UA Math 2010 spin-polarized fermions in Fabry-Pérot Rina Kanamoto

UA Math 2010 elementary excitations – bosons vs. fermions

UA Math 2010 bosonization of fermionic field

UA Math 2010 cantilever state measurement  How can we measure the quantum state of the cantilever? … No phonon counter (yet)! Idea: monitor the state of a detector atom coupled to both the field to be characterized and to an additional classical field Needed:

UA Math 2010 field state measurement in the microwave regime Wigner state tomography [Banaszek and Wodkiewicz, PRL 76, 4344 (1996)] Atomic homodyne detection [Wilkens and PM PRA 43, 3832 (1991)] MW pulse qubit Measurement LO qubit Measurement

UA Math 2010 nonlinear atomic homodyning detection of cantilever state Need: Zeeman interaction: (magnetic field gradient) (see P. Treutlein et al)

UA Math 2010 Wigner characteristic function measurement classical electromagnetic field weak cantilever excitation interaction time S. Singh + PM., arXiv v1 Initial atomic state:

UA Math 2010 measurement back-action  State of field after detection of atom in ground state: Cantilever initially in ground state

UA Math 2010 Dissipation – some numbers 6 Li atoms coupled to Si resonator: Typical lifetime of trapped atoms: 100 ms to a few seconds Dipole-allowed transitions rates: MHz to GHz Raman transitions are to virtual state:  population weighting factor  Raman decay time: a few msec MECHANICAL COUPLING Thermal dissipation: OPTICAL COUPLING