Quantum Measurement with NEMS

Transcription

1 Quantum Measurement with NEMS Michael Roukes Kavli Nanoscience Institute Physics, Applied Physics, & Bioengineering California Institute of Technology Keith Schwab Department of Physics Cornell University

2 Overview of talk Nanoelectromechanical systems (NEMS) & Quantum Electro Mechanics (QEM) the current state-of-the-art Prospects, next 5 years Future Possibilities, >5y

3 Nanoelectromechanical Systems (NEMS) Measurement of the quantum of thermal conductance 1 Nanodevice motion at microwave frequencies G(T)/16 π k B T/3h Temperature (mk) First step to quantum-limited mechanics: Quantized phononic thermal transport. K. Schwab, E.A. Henriksen, J.M. Worlock, M.L. Roukes, Nature 44, (). 1 1 Signal Amplitude (nv) T 7T 6T 5T 4T 3T Frequency (GHz) First GHz NEMS X.M.H. Huang, C. Zorman, M. Mehregany, M.L. Roukes, Nature 41, 496 (3) Multifunctional depletionmediated D-NEMS Nonlinear NEMS: Bifurcation Topology Amplifier Δ > mechanical coupling + tunable electrostatic coupling Δ < Bifurcation near transition point Response vs. DC offset + low-f AM ampl. Nanoelectromechanical logic via electrically-tunable piezoelectric coupling + crystallographic anisotropy. S.C. Masmanidis, R.B. Karabalin, I. De Vlaminck, G. Borghs, M.R. Freeman, M.L. Roukes, Science 317, 78 (7) low-f modulation signal (mv) A new paradigm for amplification via nonlinearity. R. Karabalin, S. Masmanidis, M. Matheny, R. Lifshitz, M.C. Cross, M.L. Roukes unpublished (7). 3

4 Emerging NEMS Applications Single-Electron-Spin Magnetic Resonance Detection First step to magnetic resonance imaging with atomic resolution. D. Rugar, R. Budakian, H.J. Mamin, B.W. Chui, Nature 43, 39 () Frequency Shift (Hz) Zeptogram-Scale Mass Sensing (in vacuo) NEMS shutter nozzle Time (sec) ~1 zg Frequency Shift (Hz) δ m (zg) 133 MHz 19 MHz Time (s) Mass (zeptograms) ~7 zg ~1Hz/zg First step to single-molecule mass spectrometry. Y.T. Yang, C. Callegari, X.L. Feng, K.L. Ekinci, M.L. Roukes Nano Letters 6, 583 (6) Next-Gen NEMS Nose (gas-phase sensing) Next-Gen Scanning Probes: High Frequency AFM & STM RF out RF amplifier RF in 4 db 5-Ω cable cryogenic RF amplifier 45 db directional coupler RF 5 Ω bias-t L C DC sample tip z p 1 9 Ω p STM feedback electronics V T Cryostat scanner 3.15 Displacement (a.u.) (1,).1 (1,1).5 f mn (MHz) (m +n ) 1/ (1,3) (,) (3,1) (,3) (3,) (1,4) (4,1) (3,3) A new paradigm (GC+NEMS chemisensor array) yields ultrasensitive gaseous analyte detection Mo Li, E.B. Myers, H.X. Tang, J.S. Aldridge, M.L. Roukes, unpublished (7). VHF AFM Nanocantilevers Mo Li, H.X. Tang, M.L. Roukes, Nature Nanotech., 114 (7) Frequency (MHz) Radio Frequency STM U. Kemiktarak, T. Ndukum, K.C. Schwab, K.L. Ekinci Nature (to appear, October 7) 4

5 Quantum Electro Mechanics (QEM) Cooling a NEMS resonator with quantum back-action T SET < nm-scale displacement sensing using a RF SET T N = 3K T N /T Q = 6 First demonstration of coupling NEMS to an RF SET R. Knoebel, A.N. Cleland, Nature 44, 6846 (3). T Bath T SET > T SET > S X S F T SET < T SET > γ Bath T SET < =15 h T SET > T SET < T osc (mk) 5 Nanomechanical Mode T SET < T > T SET SET > T < T < SET SET T SET > Heating γ SSET T SSET Equipartition T bath (mk) NEMS cooling/heating via SSET coupling. A. Naik, O. Buu, M.D. LaHaye, A.D. Armour, A.A. Clerk, M.P. Blencowe, K.C. Schwab, Nature 443, 718 (6). Cooling 15 V 1 V 4 V V 1 V Near-quantum-limited NEMS Detection with an RF SET T N = 16mK T N /T Q = 33 Δx/Δx QL = Frequency (MHz) Approaching the quantum limit of a NEMS resonator M. LaHaye, O. Buu, B. Camarota, K.L. Schwab, Science 34, 5667 (4) Noise power ( (μe) /Hz ) Magnitude (1-3 e) M M M Frequency (Hz) 3.8 fm/hz 1/ NR T N =73mK.5. Phase (π rads) -.5 NR NR T N =1mK First NEMS-qubit coupling (via Cooper-pair box) R IN Amplifier Mixer Tank Circuit ΓV INC VCO V INC Directional Coupler CPB Gate Resonator L T CPB GaAs C Varactor T Resonator Gate Coupled CPB / NEMS Device V drive(t) SET SET Gate C g C g NEMS-based frequency-shift CPB det n & spectroscopy M. LaHaye, J. Suh, P. Echternach, K.L. Schwab, M.L. Roukes (unpublished, 7). V g d C g CPB Spring Resonator constant k, Quality factor Q 6 4 Gate S X (fm) /Hz Y-Quadrature Modulation Vs. Fridge Temperature 5 3 mk 5 mk 4 6 mk ) V 3 7 mk (μ e d 8 mk litu p 9 mk m A 1 1 mk 11 m K 1 mk *Data offset vertically for clarity V CPB (mv) V b 5

6 Quantum Electro Mechanics (QEM) CPB-Induced Dispersive Shift: Comparison With Theory NEMS-frequency-shift-based CPB state detection and spectroscopy M. LaHaye, J. Suh, P. Echternach, K.L. Schwab, M.L. Roukes (unpublished, 7). - Data: V NR = 7. V, T mc ~ 1 mk Δf NEMS (Hz) - Theory: λ~ 1.4 MHz, T =1mK E J,max ~ 1 GHz, E C ~ 1 GHz Δf NEMS (Hz) V CPB (mv) 1 V CPB range for mean Δf NEMS (Hz) calculation V CPB (mv) 1 V CPB range for mean Δf NEMS (Hz) calculation Applied Magnetic Field (G) *model assumes.1e rms Motional smearing Applied Magnetic Field (G) - Δf NEMS (Hz) V CPB (mv) Mean Δf NEMS (Hz) -5-1 Theory Experiment Applied Magnetic Field (G) Notes: 55 Hz offset subtracted from data to compare with model; B-field sweep on top of -14 Gauss static field 6

7 Workshop on Quantum Electro Mechanics (QEM-) sponsors: Kavli Nanoscience Institute Caltech Kavli Institute at Cornell Cornell University Institute for Quantum Information Caltech Center for the Physics of Information Caltech

8 QEM prospects within reach (< 5 years) Preparing and measuring interesting quantum states: ground state, squeezed states, entangled states, superposition states. Demonstration of entanglement with qubits, entanglement with optical modes Demonstration of cavity-qed-like effects with GHz bulk-mode resonators Using these states to test models of environmental decoherence (Zurek, Habib, and Paz model) Using this system to "watch" the quantum measurement process, e.g. quantum jumps. Using mechanical resonators prepared in these states to obtain resolution beyond the standard quantum limit Use nanomechanics and nanoelectronics as ultrasensitive front end detectors for radio-frequency detection, astronomy, and security applications (NRAO and NRO) 8

9 QEM prospects within reach (< 5 years) Preparing and measuring interesting quantum states: ground state, squeezed states, entangled states, superposition states. Ground state Phase Lock-in Squeezed state Test Signal Pump FIG. 1. Block diagram of the mechanical parametric amplifier and associated measurement apparatus. The spring constant of the cantilever is modified (pumped) at frequency bytheelectric fieldfrom the capacitorplate. Mechanical parametric amplification and thermomechanical noise squeezing D. Rugar and P. Grutter, Phys. Rev. Lett. 67, (1991) Entangled state 1 [ α + α ] L R F 1 ( + ) + Ψ System = α + α L R Superposition state P[x] time Forces from Quantum Two Level Systems 1-1 N. Nuclear Spin 1-18 N. Electron Spin 1-13 N.. Charge on Cooper-Pair Box 1-9 N Flux in a SQUID ring Two-Level System x CPB best to-date (Yale): t 1 ~ 7 μs, t ~.5 μs 9

10 QEM prospects within reach (< 5 years) Demonstration of entanglement with qubits Ultra-low noise cryoamplifier Phase meter 6 GHz Stripline Resonator CPB-qubit V NR reference Mechanical Resonator NEMS/CPB/stripline resonator coupling scheme Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion Florian Marquardt, Joe P. Chen, A. A. Clerk, and S. M. Girvin Phys. Rev. Lett. 99, 939 (7) Prototype devices: Schwab Group, Cornell Total State Qubit Expectation Envelope on Ramsey interference experiment should reveal entanglement with mechanics 1 i Ψ 1 m P( n ) = 1 λ ω cos 4ECt / h + φ( α, t) e h iec () t e t / h iec / n () t e t h = α n + () t + α ( cosωmt ) [ ] Entanglement and Decoherence of a Micromechanical Resonator via Coupling to a Cooper-Pair Box A.D. Armour, M.P. Blencowe, K.C. Schwab Phys. Rev. Lett. 88, () 1

11 QEM prospects within reach (< 5 years) Demonstration of entanglement with optical modes Low photon pressure requires very soft cantilever (even after amplify dwell time with cavity) Very soft cantilever has very low frequency ~ 1KHz Low frequency cantilever has very low freezeout temperature ~ 6μK! 11

12 QEM prospects within reach (< 5 years) Demonstration of entanglement with optical modes freestanding Bragg mirror m~4ung R > 99.8% (F~4) Damping Self-cooling of a micromirror by radiation pressure S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. Hertzberg, K. Schwab, D. Bäuerle, M. Aspelmeyer, A. Zeilinger Nature 444, 67 (6). Optomechanical entanglement between a movable mirror and a cavity field D. Vitali, S. Gigan, A. Ferreira, H.R. Bohm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, M. Aspelmeyer, Phys. Rev. Lett. 98, 345 (7). (a proposal) Q ~, Cooling ratio Damping [Hz] Self-Cooling theory 3 K 3 K 1

13 QEM achievements within reach (< 5 years) Demonstration of cavity-qed-like effects with mechanical resonators Superconducting qubit storage and entanglement with nanomechanical resonators A.N. Cleland, M.R. Geller Physi. Rev. Lett. 93, 751 (4) phonon cavity modes conceptual picture of thermal relaxation: Yoctocalorimetry: Phonon Counting In Nanostructures M.L. Roukes, Physica B. 63,1 (1999) N, number of phonons in cavity 6 quantized jumps 3 N.B. Simulation from Haroche Group, Paris (photons in cavity) Time

14 τ Ν (sec) τ D (sec) QEM achievements within reach (< 5 years) Using these states to test models of environmental decoherence (e.g. Zurek, Habib, and Paz model) 1µ 1µ 1n Ψ Ψ -1 fm fm 1 fm X 1n 1 mk 1 mk 1, mk Temperature Q=5, ΔX=3ΔX SQL Zurek, Habib, Paz, Phys. Rev. Lett. 7, 1187 (1993). Lifetime for number state: τ N h = Q k T B Decoherence time for superposition of coherent states: h τ D = mγ k T Δx m B ( ) h ΔxSQL = Q k B T Δ x 14

15 QEM achievements within reach (< 5 years) Using this system to "watch" the quantum measurement process, quantum jumps. T = 5 nsec T = 1 nsec 15

16 QEM achievements within reach (< 5 years) Using mechanical resonators prepared in these states to obtain resolution beyond the standard quantum limit D.A. Harrington, R. Karabalin, MLR Degenerate, all-mechanical paramps. 17 MHz degenerate paramp 14 MHz degenerate paramp 16

17 QEM achievements within reach (< 5 years) Use nanomechanics and nanoelectronics as ultra-sensitive front end detectors for radio-frequency detection, astronomy, and security applications (NRAO and NRO) Nanomechanical resonator 5 Ω cable L T rf-set C T V g 17

18 Some longer-term QEM prospects (> 5 years) Preparing larger and larger objects into quantum states, techniques to prepare single modes of macroscopic objects into the quantum ground state Reducing the phase space for alternatives to quantum mechanics, so-called, unified dynamics theories, spontaneous collapse models Entering the parameter regime to test gravitational collapse, Penrose-like mechanism Use of mechanical mode to entangle multiple qubits Formation of "Quantum Engineering Departments" at universities with quantum limited and controlled mechanics under this domain 18

19 Some longer-term QEM prospects (> 5 years) Preparing larger and larger objects into quantum states, techniques to prepare single modes of macroscopic objects into the quantum ground state Cantilever with super-mirror Bouwmeester Group - UCSB 1 gm mirror optically cooled to 7mK Mavalvala Group - MIT 1mm X 1mm X 5nm membrane optically cooled to 7mK Harris Group - Yale 19

20 Some longer-term QEM prospects (> 5 years) Reducing the phase space for alternatives to quantum mechanics, so-called, unified dynamics theories, spontaneous collapse models Accessing the parameter regime to test gravitational collapse via Penrose-like mechanism

21 Some longer-term QEM prospects (> 5 years) Use of mechanical mode to entangle multiple qubits V V V V V V V V V V V Ew ω = 1 k ρ 4 For a 1 μm wide Diamond beam (E=1GPa): 1 GHz λ = 6 μm 1 GHz l = μm For a 1 μm wide Silicon beam (E=11GPa): 1 GHz l = 3.5 μm 1 GHz l = 1. μm cf. striplines ~1cm Coupling strength: H I = λ + ( a + a) ˆ σ x CGVG Δx ZP 7 λ = 4EC 1 ω e d 1

22 Some longer-term QEM prospects (> 5 years) Formation of "Quantum Engineering Departments" at universities with quantum limited and controlled mechanics under this domain