From trapped ions to macroscopic quantum systems

Transcription

1 7th International Summer School of the SFB/TRR21 "Control of Quantum Correlations in Tailored Matter July 2014 From trapped ions to macroscopic quantum systems Peter Rabl

2 Yesterday... Trapped ions: quantum ground state (laser cooling) cat state = x 0 x 0

3 Yesterday... Applications: Quantum computing, quantum simulators,...

4 Today... quantum ground state macroscopic objects cat state How & why? = x 0 x 0

5 Micro- & nano-mechanical systems Examples: carbon nanotube

6 Mechanical transducers force displacement

7 Mechanical transducers light charges & dipoles optical detection magnets / spins gravity displacement electric readout inertial forces... while adding little noise!

8 Micro- & nano-mechanical systems ( H. Craighead, Cornell ) precision measurement: detecting single molecules / proteins weak force measurements bio-sensors,... daily life applications: delay lines, g-sensors signal processing, data storage... ( D. Rugar, IBM ) ( Milipede, IBM )

9 Quantum mechanical systems? 10µm?

10 Quantum mechanical systems? energy... n 10 6 ~! r T 300 K cool quantum ground state

11 Passive cooling low temperature (~ 20 mk ) hni = k BT ~ r high vibration frequency! Si nano-beam (K. Schwab, Caltech) Carbon nanotubes (H. van der Zandt, Delft) SiN dilatation resonator (A. Cleland, Santa Barbara) hni 15 hni 1 hni 0

12 Laser cooling of macroscopic objects optical resonator laser optische Resonanz Energie } kinetische Energie Laser Photon vibrating mirror (~40x40 µm)

13 Optomechanical systems optical (Vienna) (Yale) (Santa Barbara) (MIT) nano-photonic... microwave a c (Lausanne)... and many more! 5 μm (Caltech) 0 1 (NIST/Jila)

14 Quantum mechanical systems O Connell et al., Nature 464, 697 (2010) ground state cooling! Teufel et al., Nature 471, 204 (2011) Chan et al., Nature 478, 89 (2011) zero point oscillations

15 Quantum mechanical systems microscopic macroscopic atoms, ions,... ~1000 atoms (M. Arndt, Vienna) ~10^12 atoms macroscopic Massive objects new physics?? Corrections to QM, wavefunction collapse,... General relativity quantum mechanics????

16 Quantum mechanical systems optical magnetic displacement electric Macroscopic quantum new applications! Mechanical quantum transducers & interfaces Q. information processing, mechanical sensing,...

17 This talk... Part I: Probing macroscopic superpositions D Part II: Electro-mechanical spin transducers magnetic tip gold wire spin qubits

18 Mechanical resonators: basics

19 Mechanical resonators N~10^12 atoms: N independent vibrational modes! Quantum system with N independent degrees of freedom! We are interested in controlling only one of those modes!

20 Mechanical resonators Elasticity theory (thin beam approximation): (A... beam cross section,... density, E... Youngs modulus)

21 Mechanical resonators Solutions: mode frequencies:

22 Mechanical resonators Solutions: mode frequencies: boundary conditions (singly clamped beam):

23 Quantized mechanical resonators

24 Quantized mechanical resonators I) Lagrangian:

25 Quantized mechanical resonators I) Lagrangian: Eigenmode expansion:

26 Quantized mechanical resonators I) Lagrangian: Eigenmode expansion: (effective mass)

27 Quantized mechanical resonators I) Lagrangian: independent harmonic oscillators! II) Canonical quantization / Hamiltonian:

28 Quantized mechanical resonators quantized displacement of the tip:

29 Quantized mechanical resonators quantized displacement of the tip: single mode approximation:

30 Coupling to other modes mechanical resonator thermal phonon reservoir

31 Coupling to other modes mechanical resonator thermal phonon reservoir The (weak) coupling to all other modes can be taken into account by a master equation: (mechanical damping rate) (thermal occupation number)

32 Thermalization & mechanical decoherence Average phonon occupation number:

33 Thermalization & mechanical decoherence Average phonon occupation number: When the mechanical mode is cooled to the ground state, it takes a time to populate it again with 1 phonon. mechanical decoherence rate:

34 Thermalization & mechanical decoherence Average phonon occupation number: When the mechanical mode is cooled to the ground state, it takes a time to populate it again with 1 phonon. mechanical decoherence rate:

35 Resonators & spin qubits

36 Quantum control of macroscopic objects 10µm?

37 Quantum control of macroscopic objects Idea: macroscopic microscopic

38 Mechanical resonators & solid state qubits lead 2e island 2e Electrostatic coupling to charge qubits. resonator superconducting loop Magnetic (Lorentz force) coupling to flux qubits. resonator mechanical resonator magnetic tip Magnetic gradient coupling to spin qubits. spin qubit quantum dot / defect center Strain coupling to quantum dots / defect centers. resonator see e.g.: P. Treutlein, C. Genes, K. Hammerer, M. Poggio, PR, arxiv:

39 NV centers in diamond Spin qubit : long coherence (T 2 T=300 K) ESR (=microwave) control Quantum optical qubit : state preparation (optical pumping) state detection (cycling transitions) spin qubit Solid state qubit : stable / no trapping requirements localized < 50 nm Nature s own trapped ion

40 Magnetic spin-resonator coupling nano-resonator magnetic tip spin qubit (NV center) MRFM (D. Rugar, IBM), BEC-resonator coupling (P. Treutlein),...

41 Magnetic spin-resonator coupling nano-resonator magnetic tip spin qubit (NV center) magnetic coupling: Zeeman shift per vibrational quanta zero point motion magnetic field gradient

42 Magnetic spin-resonator coupling h < 50nm spin qubit (NV center) magnetic coupling: zero point motion magnetic field gradient Zeeman shift per vibrational quanta

43 Magnetic spin-resonator coupling spin qubit (NV center) coherent coupling spin dephasing motional dephasing

44 Magnetic spin-resonator coupling spin qubit (NV center) coherent coupling spin dephasing motional dephasing strong coupling conditions!

45 Quantum control of mechanical motion Cooling / state preparation: motional quanta spin excitation optical pumping PR, P. Cappellaro, Gurudev Dutt, L. Jiang, J. Maze, M. Lukin, Phys. Rev. B 79, (2009).

46 Quantum control of mechanical motion Cooling / state preparation: motional quanta spin excitation optical pumping Quantum control & readout: spin superposition motional superposition map back and detect spin state PR, P. Cappellaro, Gurudev Dutt, L. Jiang, J. Maze, M. Lukin, Phys. Rev. B 79, (2009).

47 Probing macroscopic superpositions

48 Magnetometry How can I measure a small magnetic field?

49 Magnetometry How can I measure a small magnetic field? Ramsey interference measurement: i) ii) iii) iv) i) apply pi/2 pulse ii) wait iii) apply another pi/2 pulse iv) measure spin populations

50 Magnetometry i) ii) iii) iv) i)

51 Magnetometry i) ii) iii) iv) i) ii)

52 Magnetometry i) ii) iii) iv) i) ii) iii)

53 Magnetometry i) ii) iii) iv) D iv)

54 Magnetometry i) ii) iii) iv) D iv) The long coherence times of NV are used for highly sensitive magnetometers with nanoscale resolution!

55 Magnetometry for quantum signals? NV quantum magnetometer? magnetic tip D NV defect center Use Ramsey method to detect quantum field?

56 Setup two level system (qubit) detector D mechanical resonator Qubit-resonator coupling: Frequency shift ~ to resonator displacement Ramsey / magnetometry!

57 Setup two level system (qubit) detector D mechanical resonator Qubit-resonator coupling: Frequency shift ~ to resonator displacement Ramsey / magnetometry! State dependent force: quantum backaction!

58 Quantum magnetometry i) ii) iii) iv) initial resonator state

59 Quantum magnetometry i) ii) iii) iv) initial resonator state i)

60 Quantum magnetometry i) ii) iii) iv) i) ii) geometric phase

61 Quantum magnetometry i) ii) iii) iv) i) ii) geometric phase

62 Quantum magnetometry i) ii) iii) iv) i) ii) iii)

63 Quantum magnetometry i) ii) iii) iv) D

64 Quantum magnetometry i) ii) iii) iv) D iv) Probabilities:

65 Quantum magnetometry i) ii) iii) iv) D iv) Probabilities: Conditioned resonator state after the measurement:

66 Collapse and revivals... coherent rephasing 1.0 qubit population P th ( n>) entangled τ/τ m j A. Armour, M. Blencowe, K. Schwab, PRL (2002); W. Marshall, C. Simon, R. Penrose, D. Bouwmeester, PRL (2003);...

67 Collapse and revivals... coherent rephasing 1.0 qubit population P th ( n>) entangled τ/τ m j A. Armour, M. Blencowe, K. Schwab, PRL (2002); W. Marshall, C. Simon, R. Penrose, D. Bouwmeester, PRL (2003);...

68 Collapse and revivals... coherent rephasing 1.0 qubit population P th ( n>) entangled τ/τ m j driven, thermal (T=300 K) resonator! [1] S. Kolkowitz et al, Science (2012); S. Bennett et al. NJP (2012)

69 Idea: Correlations! Conditioned on the outcome of the first measurement the resonator is projected into one of the superposition states Use correlations between the first and second measurement to probe quantum superpositions over a time.

70 Idea: Correlations! Conditioned on the outcome of the first measurement the resonator is projected into one of the superposition states Use correlations between the first and second measurement to probe quantum superpositions over a time.

71 Ramsey correlation measurements

72 Ramsey correlation measurements

73 Ramsey correlation measurements Interference

74 Ramsey correlation measurements Interference geometric phase:

75 Ramsey correlation measurements Wigner function of the conditioned state correlations between the two measurements

76 Ramsey correlation measurements Wigner function of the conditioned state decoherence correlations between the two measurements

77 Ramsey correlation measurements decoherence Correlations directly probe survival/decay of macroscopic superposition states! During the waiting time the resonator is decoupled from the qubit! (high-q resonators, levitated objects!!)

78 Ramsey correlation measurements decoherence Do we really see quantum features? Correlations directly probe survival/decay of macroscopic superposition states! During the waiting time the resonator is decoupled from the qubit! (high-q resonators, levitated objects!!)

79 Leggett-Garg inequality For a macro-realistic [1] model these correlations are bound by the (Wigner type) Leggett-Garg inequality: [1] Leggett, J. Phys. Cond. Matter 14, R415 (2002); Emary, Lambert, Nori, arxiv:

80 Violation of the LG inequality Result:

81 Violation of the LG inequality Result: Maximal & robust violation of the LGI for large displacements:

82 Violation of the LG inequality Result: Interference Maximal & robust violation of the LGI for large displacements:

83 Quantum vs. classical correlations qubit reset Qubit probing a classical field: (random) trajectory, but with a specific value at each time

84 Quantum vs. classical correlations qubit reset Qubit probing a classical field: No violation! (random) trajectory, but with a specific value at each time

85 Mechanical quantum transducers

86 Solid state spin systems localized electronic (nuclear) spins weak magnetic dipole interactions environment storage times (T=300 K!!!)

87 Solid state spin systems localized electronic (nuclear) spins weak magnetic dipole interactions environment storage times (T=300 K!!!) other spins gate operations (d < 10 nm)? Jelezko, Wrachtrup, Nature Physics (2010)

88 Mechanical quantum transducer displacement magnetic tip magnetic dipole

89 Mechanical quantum transducer add charge! displacement electric dipole! magnetic dipole

90 Mechanical quantum transducer spin qubit 2 strong electrostatic coupling! spin qubit 1 long-range spin-spin interactions!

91 Wiring up mechanical resonators d 1 µm l 5 µm U U wire d 100 µm C w 0 d U U

92 Wiring up mechanical resonators direct, magnetic: 10 nm indirect: ~100 µm!! wire C w 0 d U U

93 Wiring up mechanical resonators U U U U Coupled resonator chain: collective phonon modes

94 Electro-mechanical quantum bus individual spin control collective phonon modes spin-phonon coupling

95 Electro-mechanical quantum bus trapped ion quantum computer [1] mechanical resonators artificial, massive ions

96 Phonon-mediated spin-spin interactions

97 Phonon-mediated spin-spin interactions Polaron transformation ( displaced oscillator basis ) free phonons ( phonon frequencies, mode functions ) see also proposals by C. Wunderlich, I. Cirac, etc. for trapped ion QC

98 Phonon-mediated spin-spin interactions

99 Phonon-mediated spin-spin interactions displaced oscillator basis:

100 Phonon-mediated spin-spin interactions displaced oscillator basis:

101 Phonon-mediated spin-spin interactions displaced oscillator basis: effective spin-spin interactions

102 Wiring up spins... full model: H = X n a na n 1 2 n X i(a i a i) z i X g ij (a i a i)(a j a j) ij i effective spin model: M ij H spin = X ij M ij i z j z

103 Summary & conclusions

104 Quantum mechanical systems r 1 MHz 10µm passive / active cooling New (macroscopic) quantum degree of freedom! quantum regime 2004 today

105 Probing QM at the macroscopic scale Violation of LGI with macroscopic systems: LG violation D Ramsey correlation measurements: modular variables contextuality Bell inequalities (?),... A. Asadian, C. Brukner, PR, PRL 112, (2014)

106 Mechanical quantum transducers macroscopic & quantum optical magnetic displacement electric Coherent interface between electric, magnetic & optical quantum system!

107 Mechanical quantum transducers magnetic tip gold wire Electro-mechanical spin-spin interactions. PR et al, Nature Physic (2010) spin qubits Qubit-light-interfaces. K. Stannigel et al, PRL (2010) A. H. Safavi-Naeini, O. Painter, NJP (2011) superconducting qubit optical cavity membrane capacitor Experiments: Caltech, NIST/JILA, Copenhagen, Santa Barbara,...

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