Download presentation
Presentation is loading. Please wait.
1
Quantum Optics in Circuit QED:
From Single Photons to Schrodinger Cats…. Rob Schoelkopf, Applied Physics, Yale University PI’s: RS Michel Devoret Luigi Frunzio Steven Girvin Leonid Glazman Postdocs & grad students wanted!
2
Thanks to cQED Team Thru the Years!
Steve Girvin, Michel Devoret, Luigi Frunzio, Leonid Glazman Theory Experiment (present) Alexandre Blais Lev Bishop Jay Gambetta Jens Koch Eran Ginossar Nunnenkamp G. Catelani Lars Tornberg Terri Yu Simon Nigg Dong Zhou Mazyar Mirrahimi Zaki Leghtas Experiment (past) Hanhee Paik Luyan Sun Gerhard Kirchmair Matt Reed Adam Sears Brian Vlastakis Eric Holland Matt Reagor Andy Fragner Andrei Petrenko Jacob Blumhoff Teresa Brecht Andreas Wallraff Dave Schuster Andrew Houck Leo DiCarlo Johannes Majer Blake Johnson Jerry Chow Joe Schreier
3
Outline Cavity QED vs. Circuit QED
How coherent is a Josephson junction? Scaling the 3D architecture A bit of nonlinear quantum optics Deterministic Schrödinger cat creation
4
Cavity Quantum Electrodynamics (cQED)
2g = vacuum Rabi freq. k = cavity decay rate g = “transverse” decay rate Strong Coupling = g > k , g Jaynes-Cummings Hamiltonian Describe diagram Describe each rate Describe each term in Hamiltonian Discuss strong coupling Electric dipole Interaction Dissipation Quantized Field 2-level system
5
2012: Year of Quantum Measurement
"for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems" Serge Haroche (ENS/Paris) Dave Wineland (NIST-Boulder) Cavity QED w/ Rydberg atoms Quantum jumps w/ trapped ions
6
Qubits Coupled with a Quantum Bus
use microwave photons guided on wires! “Circuit QED” transmission line “cavity” out Josephson-junction qubits 7 GHz in Thy: Blais et al., Phys. Rev. A (2004)
7
Superconducting Qubits
Transmon Cj Lj Superconductor 1 nm Insulating barrier C Energy Superconductor (Al) nonlinearity from Josephson junction (dissipationless) electromagnetic oscillator Engineerable spectrum Lithographically produced features Each qubit is an “individual” Decoherence mechanisms? See reviews: Devoret and Martinis, 2004; Wilhelm and Clarke, 2008
8
Advantages of 1d Cavity and Artificial Atom
Vacuum fields: mode volume zero-point energy density enhanced by Transition dipole: x 10 larger than Rydberg atom L = l ~ 2.5 cm Supports a TEM mode like a coax: coaxial cable 5 mm
9
Advantages of 1d Cavity and Artificial Atom
Vacuum fields: mode volume zero-point energy density enhanced by Transition dipole: x 10 larger than Rydberg atom compare Rydberg atom or optical cQED: Circuit QED much easier to reach strong interaction regimes!
10
The Chip for Circuit QED
Nb Qubit trapping easy: it’s “soldered” down! Si Al Nb Expt: Wallraff et al., Nature (2004)
11
Cavity QED: Resonant Case
vacuum Rabi oscillations # of photons “phobit” qubit state “dressed state ladders” “quton” (see e.g. “Exploring the Quantum…,” S. Haroche & J.-M. Raimond)
12
Strong Resonant Coupling: Vacuum Rabi Splitting
g >> [k, g] 2g ~ 350 MHz Can achieve “Fine-Structure Limit” Cooperativity: Review: RS and S.M. Girvin, Nature 451, 664 (2008). Nonlinear behavior: Bishop et al., Nature Physics (2009).
13
But does it “compute”? Algorithms: DiCarlo et al., Nature 460, 240 (2009).
14
cavity: “entanglement bus,” driver, & detector
A Two-Qubit Processor 1 ns resolution DC - 2 GHz T = 10 mK cavity: “entanglement bus,” driver, & detector transmon qubits
15
General Features of a Quantum Algorithm
Qubit register M Working qubits create superposition encode function in a unitary process measure initialize will involve entanglement between qubits Maintain quantum coherence 1) Start in superposition: all values at once! 2) Build complex transformation out of one-qubit and two-qubit “gates” 3) Somehow* make the answer we want result in a definite state at end! *use interference: the magic of the properly designed algorithm
16
Grover Algorithm Step-by-Step
The correct answer is found >80% of the time! Coherence time ~ 1 ms Total pulse sequence: 104 nanoseconds Previously implemented in NMR: Chuang et al., 1998 Ion traps: Brickman et al., 2003 Linear optics: Kwiat et al., 2000
17
Will it ever scale? or, “Come on, how coherent could this squalid-state thing ever really get?” (H. Paik et al., PRL, 2011)
18
Progress in Superconducting Charge Qubits
Schoelkopf’s Law: Coherence increases x every 3 years! Similar plots can probably be made for phase, flux qubits
19
Materials: Dirt Happens!
Dolan Bridge Technique PMMA/MAA bilayer Al/AlOx/Al Qubit: two 200 x 300 nm junctions Rn~ 3.5 kOhms Ic ~ 40 nA Current Density ~ A/cm2
20
“participation ratio” = fraction of energy stored in material
Why Surfaces Matter… + - E d a-Al2O3 Nb 5 mm “participation ratio” = fraction of energy stored in material even a thin (few nanometer) surface layer will store ~ 1/1000 of the energy If surface loss tangent is poor ( tand ~ 10-2) would limit Q ~ 105 Increase spacings decreases energy on surfaces increases Q as shown in: Gao et al (Caltech) O’Connell et al (UCSB) Wang et al (UCSB)
21
One Way to Be Insensitive to Surfaces…
3-D waveguide cavity machined from aluminum (6061-T6, Tc ~ 1.2 K) TE101 fundamental mode 50 mm Increased mode volume decreases surface effects! Observed Q’s to 5 M
22
Transmon Qubit in 3D Cavity
Vacuum capacitor ~ mm g 100 MHz 50 mm Smaller fields compensated by larger dipole Still has same net coupling!
23
Coherence Dramatically Improved
Dt p T1 = 60 ms meas. p/2 Dtp/2 T2 = 14 ms Dtp/2/2 p/2 p Techo = 25 ms
24
Ramsey Experiment/Hahn Echo
T2echo = 145 ms
25
Remarkable Frequency Stability
f01 = (608) Hz Overall precision after 12 hours: ~ 19 Hz or 3 ppb No change in Hamiltonian parameters > 80 ppb in 12 hours!?
26
Charge Qubit Coherence, Revised
QEC limit? Schoelkopf’s law 10x every 3 years!
27
Milliseconds and Beyond?
0.6 Billion Ringdown of TE011 Fit (Black): τ = 3.7ms QL=ωτ=265M best qubits E Now this is a Quantum Memory for qubits!! M. Reagor et. al. to be published
28
Building Blocks for Scaling
Many Atoms Many Cavities One Atom One Cavity Two Atoms One Cavity One Atom Two Cavities
29
Two-Cavity Design 45mm 500nm 1.2mm 900μm Al2O3
30
Strong dispersive limit: QND measurement of single photons
Algorithms: DiCarlo et al., Nature 460, 240 (2009).
31
Dispersive Limit of cQED
“phobit” Diagonalizing J-C Hamilt.: qubit cavity “quton” Dispersive (D>>g):
32
Photon Numbersplitting
Strong Dispersive Hamiltonian: “doubly-QND” interaction n=2 n=2 n=1 qubit absorption n=1 n=0 n=0 Qubit Frequency (GHz)
33
QND Measurement of Photon Number
Quantum “go-fish” “Got any ‘s? “Click!” cavity g e 2) then measure qubit state using second cavity g qubit 1) perform n-dependent flip of qubit Repeated QND of n=0 or n=1: B. Johnson, Nature Phys., 2010
34
Coherent Displacements
create Photon populations as a function of photon number Show pulse sequence One fitting parameter
35
Coherent Displacements
Photon populations as a function of photon number Show pulse sequence One fitting parameter
36
Using a cavity as a memory: Schrodinger cats on demand
experiment theory G. Kirchmair M. Mirrahimi B. Vlastakis Z. Leghtas “No, no mini-Me, we don’t freeze our kitty!”
37
Driving a Quantum Harmonic Oscillator
Giving a classical ‘drive’ to a quantum system: Phase-space portrait of oscillator state: Where: with Our state is described by two continuous variables, an amplitude and phase. A ‘coherent’ state.
38
What’s a Coherent State?
x Glauber (coherent) state x
39
What’s a Coherent State?
x Glauber (coherent) state x
40
What’s a Coherent State?
x Glauber (coherent) state x
41
Measured Q functions of a Coherent State
Q functions with various displacements Proof! g e g
42
Deterministic Cat Creation
cavity qubit
43
Deterministic Cat Creation
cavity qubit
44
Deterministic Cat Creation
cavity transmission w 5ns pulse cavity qubit
45
Deterministic Cat Creation
cavity qubit
46
Deterministic Cat Creation
cavity qubit
47
Deterministic Cat Creation
cavity qubit
48
Deterministic Cat Creation
cavity qubit
49
Deterministic Cat Creation
cavity qubit
50
So, What’s a Cat State? E x Schrödinger cat state x
Superposition with distinguishability, D
51
So, What’s a Cat State? E x Schrödinger cat state x
What happens now, when packets collide?
52
Seeing the Interference: Wigner Function
Parity Thy: Negative fringes = “whiskers” Expt’l. Wigner tomography: Leibfried et al., 1996 ion traps (NIST) Haroche/Raimond , 2008 Rydberg (ENS) Hofheinz et al., 2009 in circuits (UCSB)
53
Seeing the Interference: Wigner Function
Da cavity 1 map qf Xp/2 wait Xp/2 qubit cavity 2 measurement
54
Wigner Function: Interpretation
x
55
Wigner Function: Interpretation
x
56
Fringes for different cat sizes
57
Z. Leghtas ,M. Mirrahimi et.al. arXiv. 1207.0679 (2012)
Creating Curious Cats State used for a protected memory multicomponent interference fringes Z. Leghtas ,M. Mirrahimi et.al. arXiv (2012)
58
Curiouser and Curiouser…
Y “Bulldog State?”
59
So Now What? “Age of Qu. Error Correction.” “Age of Qu. Feedback.”
“Age of Measurement.” “Age of Entanglement” “Age of Coherence”
60
So Now What? Coherence won’t be the reason it doesn’t work…
In next few years, we will be building non-trivial (i.e. non-calculable) quantum systems from the “bottom-up” Beginning era of “active” quantum devices – incorporating: – quantum feedback – quantum error-correction – engineered dissipation Advent of analog quantum simulations and artificial many-body physics? What (if any?) are the medium-term applications of quantum information technology?
61
Error Correction with Minimal Hardware
Leghtas, Mirrahimi, et al., arXiv 1207:0679 Correction for a single bit / phase flip: at least 5 qubits A single cavity mode: infinite dimensional Hilbert Space Minimal QEC hardware: a single cavity mode coupled to a qubit Idea: encode a qubit in a 4 component parity state also known as a Zurek “compass state” Then photon loss can be monitored/corrected by repeated photon parity measurement using qubit
62
Numerical simulations
63
Circuit QED Team Members 2012
Gerhard Kirchmair Luyan Sun Andrei Petrenko Matt Reed Nissim Ofek Matt Reagor Eric Holland Adam Sears Teresa Brecht Jacob Blumhoff Brian Vlastakis Kevin Chou Luigi Frunzio Hanhee Paik Andreas Fragner Steve Girvin M. Mirrahimi Z. Leghtas Leonid Glazman Michel Devoret Funding:
64
Summary 3D approach has led to 2+ orders of magnitude improvements!
Paik et al., PRL 107, (2011). We won’t be able to use coherence as an excuse anymore! Qubits: T2 ~ 2*T1 ~ sec Cavities: T1 ~ 0.01 sec New physics: single-photon Kerr and dispersive revivals Kirchmair, Vlastakis et al., in preparation. New approaches: cats in cavities as logical qubits! Leghtas, Mirrahimi et al., ArXiv: and ArXiv:
Similar presentations
