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Cavity Optomechanics: a Playground for Quantum Physics

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Cavity Optomechanics: a Playground for Quantum Physics Cavity optomechanics: a playground for quantum physics David Vitali School of Science and Technology, Physics Division, University of Camerino, Italy, THE GROUP: COLLABORATION with M. Asjad, M. Abdi, M. Bawaj, Sh. Barzanjeh, C. Biancofiore, G.J. Milburn, G. Di Giuseppe, M.S. Kim, M. Karuza, G.S. Agarwal R. Natali, P. Tombesi 1 Cavity Optomechanics, Innsbruck, Nov 04 2013 Outline of the talk 1. Introduction to cavity optomechanics: the membrane- in-the-middle (MIM) setup as paradigmatic example 2. Proposal for generating nonclassical mechanical states in a quadratic MIM setup 3. Controlling the output light with cavity optomechanics: i) optomechanically induced transparency (OMIT); ii) ponderomotive squeezing 4. Proposal for a quantum optomechanical interface between microwave and optical signals 2 INTRODUCTION Micro- and nano-(opto)-electro-mechanical devices, i.e., MEMS, MOEMS and NEMS are extensively used for various technological applications : • high-sensitive sensors (accelerometers, atomic force microscopes, mass sensors….) • actuators (in printers, electronic devices…) • These devices operate in the classical regime for both the electromagnetic field and the motional degree of freedom However very recently cavity optomechanics has emerged as a new field with two elements of originality: 1. the opportunities offered by entering the quantum regime for these devices 2. The crucial role played by an optical (electromagnetic) cavity 3 Why entering the quantum regime for opto- and electro-mechanical systems ? 1. quantum-limited sensing, i.e., working at the sensitivity limits imposed by Heisenberg uncertainty principle VIRGO (Pisa) Nano-scale: Single-spin MRFM Macro-scale: gravitational wave D. Rugar group, IBM Almaden interferometers (VIRGO, LIGO) Detection of extremely weak forces and tiny displacements 4 2. exploring the boundary between the classical macroscopic world and the quantum microworld (how far can we go in the demostration of macroscopic quantum phenomena ?) Optical detection of Schrodinger cat states of a cantilever Cat states of optically levitated nanospheres (O. Romero-Isart, et al., Phys. Rev. Lett. 107, 020405 (2011). 5 3. quantum information applications (optomechanical devices as light-matter interfaces and transducers for quantum computing architectures, or long-distance quantum communication optimal solid state qubits – optical photon transducer K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, PRL 105, 220501 (2010) 6 A large variety of cavity optomechanical devices 1. Fabry-Perot cavity with a moving micromirror micropillar Monocrystalline mirror Si cantilever, (Heidmann, (Aspelmeyer, Paris) Vienna) 2. Silica toroidal optical microcavities spoke-supported With microresonator electronic (Vahala-Caltech, Kippenberg, actuation, EPFL) (Bowen, Brisbane) 7 microdisk and a vibrating nanomechanical beam waveguide (Yale, H.Tang) Evanescent coupling of a SiN nanowire to a Radiation-pressure Silicon nanobeam toroidal microcavity or dipole gradient (Kippenberg, EPFL) photonic optomechanical coupling cavity (Painter, Caltech) “membrane in the middle” scheme: Fabry-Perot cavity with a thin SiN membrane inside (J. Harris-Yale, Kimble-Caltech, Camerino, Regal-JILA) 8 CIRCUIT-CAVITY-ELECTROMECHANICS Microwave cavity with nanomechanical beams (Sillanpaa, Helsinki) Capacitive coupling with the mechanical element Microwave cavity with membrane capacitor, Tuefel, Boulder Microwave cavity with nanomechanical beams (Schwab, Caltech) 9 ATOMIC CAVITY OPTOMECHANICS BEC mechanical oscillations within a Fabry-Perot cavity Stamper-Kurn, Berkeley, Esslinger, Zurich Treutlein, Basel 10 The membrane-in-the-middle setup Many cavity modes (still Gaussian TEMmn for an aligned membrane close to the waist) Hcav k z0 ak ak k Many vibrational modes nx my u (x,y) of the membrane u x, y sin sin mn mn d d T 2 2 T = surface tension nm 2 m n = SiN density, Ld d Ld = membrane thickness d = membrane side length 11 Vibrational frequencies m,n = 1,2… Simplified description: single mechanical oscillator, nonlinearly coupled to a single optical oscillator Possible when: • The external laser (with frequency L c) drives only a single cavity mode a and scattering into the other cavity modes is negligible (no frequency close mode) • A bandpass filter in the detection scheme can be used, isolating a single mechanical resonance Hˆ m p2 q2 qaa H 2 drive detection bandwidth Cavity optomechanics Hamiltonian Hˆ i Ee iLt a E*eiLt a valid for a wide variety of systems drive 2P E L amplitude of the driving laser with input power P 12 L L TUNABLE OPTOMECHANICAL INTERACTION by changing membrane position and orientation Radiation pressure interaction first order expansion of (q) q c G0q Poor approximation at nodes and antinodes (where the dependence is quadratic) (Thompson et al., Nature 2008) q 1p arcsin R cos2k z q 0 0 0 OPTICAL MODE SPECTROSCOPY for a perfectly aligned membrane with reflectivity R=0.2, placed close to the waist 13 Membrane misalignment (and shift from the waist) couples the TEMmn cavity modes via scattering Splitting of degenerate modes and avoided crossings linear combinations of nearby TEMmn modes become the new cavity modes: (q) is changed significantly: tunable optomechanical interaction (J.C. Sankey et al., Nat. Phys. 2010) Crossing between the TEM00 singlet and the TEM20 triplet Experimental cavity frequencies with 0.21 mrad misalignment (M. Karuza et al., J. Opt. 15 (2013) 025704) 14 Enhanced quadratic interaction at an avoided crossing Flowers-Jacobs et al. APL, 2012 Results in a very short fiber-based cavity setup at Yale. q 20GHz/ nm2 2 Recent results in our setup 2 H qq a a quadratic “dispersive” 17 int coupling WHAT TO DO WITH A QUADRATIC INTERACTION HAMILTONIAN ? i) Generation of mechanical Schrodinger cat states through reservoir engineering (M. Asjad and D. Vitali, arXiv:1308.0259) ii) Generation of mechanical squeezing via optical spring kicks (M. Asjad et al., arXiv:1309.5485) 18 RESERVOIR ENGINEERING Dynamics driven by an effective dissipative generator, with a nonclassical steady state ∞ (target state) (Poyatos et al., 1993, generalization in Verstraete et al., 2009, Diehl et al., 2008) “Target state” Typical solution = Lindblad generator such that C 0 Engineered dynamics which must dominate over undesired ones 19 EXAMPLES C bˆ bˆ Generation of entangled two-mode squeezed state of 1 2 two continuous variable (CV) systems : 1. Entangled atomic ensembles through engineered optical reservoir (experiment by Krauter et al., PRL 2011) 2. Entangled cavity modes through engineered atomic reservoir (Pielawa et al., PRL 2007) 3. Entangled mechanical resonators in cavity optomechanics (Tan et al. PRA 2013) C bˆ bˆ Generation of single-mode squeezed state 1. Motion of Trapped ions (Carvalho, et al., PRL 2001) 2. Squeezed mechanical resonators in cavity optomechanics (Kronwald et al. , 2013) 20 ˆ 2 Generation of entangled cat states of two C1 aˆb ˆ cavity modes with amplitude C2 aˆ b (through engineered atomic reservoirs, Arenz et al., 2013) Here we engineer the “optical mode reservoir” in cavity optomechanics for robust generation of a mechanical Schrodinger cat states with amplitude ˆ2 2 with C b (M. Asjad and D. Vitali, arXiv:1308.0259) (see also in trapped ions motion (Carvalho et al. 2001) and also H. Tan et al., PRA 2013) 21 One needs quadratic optomechanical coupling and a bichromatic driving (pump on the second red sideband) Linearization around steady state a s a + rotating wave approximation 2 E1 i * g2 s Adiabatic elimination of cavity mode effective dissipative dynamics for the mechanical resonator 22 One has to beat the undesired standard thermal reservoir coupled with damping rate gm The cat generation is possible at transient time t ≈ 1/G, if G » gmn C bˆ2 2 Fidelity Fmax = 0.999 starting from precooled ground state m ≈ |0><0| 7 m =10 MHz, T=10 mK nT = 100, Qm = 10 23 Ground state pre-cooling requires linear coupling and driving at the first red sideband fast switching from linear to quadratic interaction Using only quadratic coupling: we first cool with two-phonon cooling (E1 = = 0) and then switch on the resonant pump E1. When G » gmn, one cools down to m ≈ 0.75 |0><0| + 0.25 |1><1| (Nunnenkamp et al. PRA 2010) and cat state generation is good also in this case. 24 Fidelity Fmax = 0.94 starting from two-photon cooled state m ≈ 0.75 |0><0| + 0.25 |1><1| Time evolution very well approximated by a “decohering cat” state Decoherence rate Such a scheme is ideal to test decoherence models (i.e., environmental decoherence versus collapse models….) on nanomechanical resonators (M. Asjad and D. Vitali, arXiv:1308.0259) 25 Open loop controls: “Optical spring kicks” for stationary mechanical squeezing Pulsed driving laser E(t) t t Pulsed intracavity kicking the potential stiffness photon number |(t)|2 1/ t Short “bad” cavity fast kicks 26 Taking into account thermal noise and damping, one gets a stationary purified mechanical squeezed state (~13 dB) , even if starting from the equilibrium thermal state nth = 10 minimum variance, in the case when the pulse area fluctuates randomly from kick to kick (0.3% level) M. Asjad et al., arXiv:1309.5485 Time evolution of purity, entropy 27 and occupancy The stationary state is much less pure, when starting from the equilibrium thermal state nth = 200, even though still 0.8 dB of squeezing M. Asjad et al., arXiv:1309.5485 28 EFFECTS OF THE MECHANICAL RESONATOR ON THE OPTICAL FIELD I. EXPERIMENTS ON OPTOMECHANICALLY
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