quantum imaging: ghost imaging and quantum...

Quantum Optomechanical Cavity

Shabir BarzanjehInstitute of science and technology(IST) Austria

IPM-Tehran (29.12.2016) 1

Presentation outline

Mechanical resonatorsRadiation pressureOptomechanical cavityMicrowave cavity and electromechanicsTheory of the Optomechanical cavity/cooling

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Presentation outline

Mechanical resonatorsRadiation pressureOptomechanical cavityMicrowave cavity and electromechanicsTheory of the Optomechanical cavity/cooling

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Mechanical resonatorsVibrational modes of any object is given by Euler beam theory

Rev. Mod. Phys. 86, 1391(2014) 4

Mechanical resonatorsVibrational modes of any object is given by Euler beam theory

damping external forces

Rev. Mod. Phys. 86, 1391(2014) 5

Mechanical resonatorsVibrational modes of any object is given by Euler beam theory

damping external forces

Rev. Mod. Phys. 86, 1391(2014) 6

Mechanical resonatorsVibrational modes of any object is given by Euler beam theory

damping external forces

the spread of the coordinate in the ground-state

mechanical vacuum state

Rev. Mod. Phys. 86, 1391(2014) 7

Mechanical resonatorsVibrational modes of any object is given by Euler beam theory

damping external forces

the spread of the coordinate in the ground-state

mechanical vacuum state

Rev. Mod. Phys. 86, 1391(2014) 8

ttttiional modes of any object is given by Euler beam theory

damping external

average phonon number of the environment

Effect of dissipation

Rev. Mod. Phys. 86, 1391(2014) 9

average phonon number of the environment

Rate of heating out from ground state

Effect of dissipation

Rev. Mod. Phys. 86, 1391(2014) 10Cold particle in the box

average phonon number of the environment

Rate of heating out from ground state

Effect of dissipation

Rev. Mod. Phys. 86, 1391(2014) 11

average phonon number of the environment

Rate of heating out from ground state

Effect of dissipation

Rev. Mod. Phys. 86, 1391(2014)

average phooooooooooooooooooooooooooooo

• Viscous damping• Clamping losses

• Thermoelastic damping and phonon-phonon interactions

• Materials-induced losses

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average phonon number of the environment

Rate of heating out from ground state

Effect of dissipation

Rev. Mod. Phys. 86, 1391(2014)

average phooooooooooooooooooooooooooooo

• Viscous damping• Clamping losses

• Thermoelastic damping and phonon-phonon interactions

• Materials-induced losses

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Cryogenic temperature ~7mk

ent

Noise spectrum of a damped mechanical resonator

One measures the motion of a single harmonic oscillator in thermal equilibrium, one will observe a trajectory x(t) oscillating at the eigenfrequencyΩm.

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Noise spectrum of a damped mechanical resonator

One measures the motion of a single harmonic oscillator in thermal equilibrium, one will observe a trajectory x(t) oscillating at the eigenfrequencyΩm.

Mechanical damping and the fluctuating thermal Langevin force lead to:

A randomly time-varying amplitude and phase

Amplitude and phase change on the time scale

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Noise spectrum of a damped mechanical resonator

One measures the motion of a single harmonic oscillator in thermal equilibrium, one will observe a trajectory x(t) oscillating at the eigenfrequencyΩm.

Mechanical damping and the fluctuating thermal Langevin force lead to

A randomly time-varying amplitude and phase

Amplitude and phase change on the time scale

Europhys. Lett. 47, 545(1999)

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Noise spectrum of a damped mechanical resonator

One measures the motion of a single harmonic oscillator in thermal equilibrium, one will observe a trajectory x(t) oscillating at the eigenfrequencyΩm.

Mechanical damping and the fluctuating thermal Langevin force lead to

A randomly time-varying amplitude and phase

Amplitude and phase change on the time scale

Europhys. Lett. 47, 545(1999)

noise power spectral density

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Quantum regime

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Why mechanical resonators? applications

Bridges different systems with different charactristics [Phys. Scr. T 137 014001(2009)]:a. Coupling with several qubits: atom, ion, and molecule

b. Coupling with BECs

c. Superconducting qubits(transmon)

Quantum information processing [Phys. Rev. Lett. 110, 120503(2013)]

Optical-microwave conversion [ShB, Phys. Rev. Lett. 109, 130503 (2012)]

Strong Nonlinearity [Phys. Rev. B 67 134302 (2003)]

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Why mechanical resonators? applications

Bridges different systems with different charactristics [Phys. Scr. T 137 014001(2009)]:a. Coupling with several qubits: atom, ion, and molecule

b. Coupling with BECs

c. Superconducting qubits(transmon)

Quantum information processing [Phys. Rev. Lett. 110, 120503(2013)]

Optical-microwave conversion [ShB, Phys. Rev. Lett. 109, 130503 (2012)]

Strong Nonlinearity [Phys. Rev. B 67 134302 (2003)]

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Why mechanical resonators? applications

Bridges different systems with different charactristics [Phys. Scr. T 137 014001(2009)]:a. Coupling with several qubits: atom, ion, and molecule

b. Coupling with BECs

c. Superconducting qubits(transmon)

Quantum information processing [Phys. Rev. Lett. 110, 120503(2013)]

Optical-microwave conversion [ShB, Phys. Rev. Lett. 109, 130503 (2012)]

Strong Nonlinearity [Phys. Rev. B 67 134302 (2003)]

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Why mechanical resonators? applications

Bridges different systems with different charactristics [Phys. Scr. T 137 014001(2009)]:a. Coupling with several qubits: atom, ion, and molecule

b. Coupling with BECs

c. Superconducting qubits(transmon)

Quantum information processing [Phys. Rev. Lett. 110, 120503(2013)]

Optical-microwave conversion [ShB, Phys. Rev. Lett. 109, 130503 (2012)]

Strong Nonlinearity [Phys. Rev. B 67 134302 (2003)]

22

Why mechanical resonators? applications

Bridges different systems with different charactristics [Phys. Scr. T 137 014001(2009)]:a. Coupling with several qubits: atom, ion, and molecule

b. Coupling with BECs

c. Superconducting qubits(transmon)

Quantum information processing [Phys. Rev. Lett. 110, 120503(2013)](Memory, repeater)

Optical-microwave conversion [ShB, Phys. Rev. Lett. 109, 130503 (2012)]

Strong Nonlinearity [Phys. Rev. B 67 134302 (2003)]

23

Why mechanical resonators? applications

Bridges different systems with different charactristics [Phys. Scr. T 137 014001(2009)]:a. Coupling with several qubits: atom, ion, and molecule

b. Coupling with BECs

c. Superconducting qubits(transmon)

Quantum information processing [Phys. Rev. Lett. 110, 120503(2013)]

Optical-microwave conversion [ShB, Phys. Rev. Lett. 109, 130503 (2012)]

Strong Nonlinearity [Phys. Rev. B 67 134302 (2003)]

24

Why mechanical resonators? applications

Bridges different systems with different charactristics [Phys. Scr. T 137 014001(2009)]:a. Coupling with several qubits: atom, ion, and molecule

b. Coupling with BECs

c. Superconducting qubits(transmon)

Quantum information processing [Phys. Rev. Lett. 110, 120503(2013)]

Optical-microwave conversion [ShB, Phys. Rev. Lett. 109, 130503 (2012)]

Strong Nonlinearity [Phys. Rev. B 67 134302 (2003)]

25

Why mechanical resonators? applications

Bridges different systems with different charactristics [Phys. Scr. T 137 014001(2009)]:a. Coupling with several qubits: atom, ion, and molecule

b. Coupling with BECs

c. Superconducting qubits(transmon)

Quantum information processing [Phys. Rev. Lett. 110, 120503(2013)]

Optical-microwave conversion [ShB, Phys. Rev. Lett. 109, 130503 (2012)]

Strong Nonlinearity [Phys. Rev. B 67 134302 (2003)]

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We need mechanical cooling

Presentation outline

Mechanical resonatorsRadiation pressureOptomechanical cavityMicrowave cavity and electromechanicsTheory of the Optomechanical cavity/cooling

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Radiation pressure Simplest form of radiation pressure coupling is the momentum transfer due to reflection.

Single photon transfers the momentum

the cavity round trip time

the radiation pressure force caused by one intracavity photon

Rev. Mod. Phys. 86, 1391(2014) 30

Presentation outline

Mechanical resonatorsRadiation pressureOptomechanical cavityMicrowave cavity and electromechanicsTheory of the Optomechanical cavity/cooling

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Optomechanical cavity

Rev. Mod. Phys. 86, 1391(2014) 32

Optomechanical cavity

Rev. Mod. Phys. 86, 1391(2014) 33

Optomechanical cavity

1ng mass and 1MHz frequency

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Optomechanical cavity

1ng mass and 1MHz frequency

Rev. Mod. Phys. 86, 1391(2014) 35

Optomechanical cavity

Rev. Mod. Phys. 86, 1391(2014) 36

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Presentation outline

Mechanical resonatorsRadiation pressureOptomechanical cavity

Microwave cavity and electromechanicsTheory of the Optomechanical cavity/cooling

IPM-Dec 2016 39

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Si3N4 electromechanics

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Si3N4 electromechanics

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Si3N4 electromechanics

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Si3N4 electromechanics

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SOI electromechanics

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Presentation outline

Mechanical resonatorsRadiation pressureOptomechanical cavityMicrowave cavityTheory of the Optomechanical cavity/cooling

IPM-Dec 2016 53

Cooling

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Cooling

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Cooling

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Cooling

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Optomechanical Quantum equations of motion

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Optomechanical Quantum equations of motion

Optomechanical Classical equations of motion

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Optomechanical Quantum equations of motion

Optomechanical Classical equations of motion

no vacuum fluctuations

Classical random force

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Optomechanical Quantum equations of motion

Optomechanical Classical equations of motion

no vacuum fluctuations

Classical random force

multistability, self induced oscillations, chaos,…

l i bil61

Linearization Analyze the quantum dynamics around classical mean values due to classical random forces and quantum noise on mirror and cavity

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Linearization Analyze the quantum dynamics around classical mean values due to classical random forces and quantum noise on mirror and cavity

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Linearization Analyze the quantum dynamics around classical mean values due to classical random forces and quantum noise on mirror and cavity

Small nonlinear term

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Linearization Analyze the quantum dynamics around classical mean values due to classical random forces and quantum noise on mirror and cavity

Small nonlinear term

naaaaaaalyze the quantum dynamics around classical mean values due to classical rrrrrrrrdddddddd quantum noise on mirror and cavity

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Optomechanical cooling

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Optomechanical cooling

Anti-Stokes scattering

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Optomechanical cooling

Anti-Stokes scattering

Stokes scattering

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Optomechanical cooling

Anti-Stokes scattering

Stokes scattering

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Optomechanical cooling

Anti-Stokes scattering

Stokes scattering

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Optomechanical cooling

Anti-Stokes scattering

Stokes scattering

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Optomechanical cooling

Anti-Stokes scattering

Stokes scattering

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Cavity field mediates mechanical cooling, weak coupling regime

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Cavity field mediates mechanical cooling, weak coupling regime

backaction

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Cavity field mediates mechanical cooling, weak coupling regime

backaction

Optical spring effect(softening)

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Conclusion Applications of mechanical resonatorsPhysic of mechanical resonatorsOptomechanical cavitiesMicrowave eletromechanicsOptomechanical cooling

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low-pressure chemical vapor deposition(LPCVD)

(i) LPCVD of stoichiometric Si3N4 on both sides of a 200 μm thick silicon substrate, (ii) C4F8:SF6 plasma etch through the nitride membrane defining the mechanical beam resonator and pull-in cuts on the top side, and membrane windows on the bottom side,(iii) electron beam lithography, aluminum deposition, and lift-off steps to pattern the microwave circuit(iv) final release of the nitride membrane using a silicon-enriched tetramethylammoniumhydroxide (TMAH) solution

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1 cm × 1 cm chips diced from a high-resistivity siliconon-insulator (SOI) wafer manufactured by SOITEC usingthe Smart Cut process [22]. The SOI wafer consists ofa 300 nm thick silicon device layer with (100) surfaceorientation and p-type (Boron) doping with a specifiedresistivity of 500 Ω-cm. Underneath the device layer isa 3 μm buried silicon dioxide (SiO2) BOX layer. Thedevice and BOX layers sit atop a silicon (Si) handle waferof thickness 675 μm and a specified resistivity of 750 Ω-cm. Both the Si device layer and handle wafer are grownusing the Czochralski crystal growth method.Fabrication of the coupled coil resonator and H-slotresonator can be broken down into the following six steps.In step (1), we pattern the H-slot resonator using electron beam (e-beam) lithography in ZEP-520A resist, andetch this pattern into the Si device layer using an inductively coupled plasma reactive ion etch (ICP-RIE). Afterthe ICP-RIE etch, we clean the chips with a 4 min piranha bath and a 12 sec buffered hydrofluoric acid (BHF)dip. In step (2), we pattern the capacitor electrodes andground plane region using ZEP-520A resist and use electron beam evaporation to deposit 60 nm of Al on thechip. In step (3), we define a protective scaffold formedout of LOR 5B e-beam resist to create the crossover re-

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