Interaction between surface acoustic waves and a transmon qubit

Transcription

1 Interaction between surface acoustic waves and a transmon qubit Ø Introduction Ø Artificial atoms Ø Surface acoustic waves Ø Interaction with a qubit on GaAs Ø Nonlinear phonon reflection Ø Listening to a decaying atom Ø Interaction with a qubit on LiNbO 3 Ø Controllable coupling Ø Lamb shift due to the phonon vacuum Ø Ongoing experiments Ø Summary M.V. Gustafsson et al., Science 346, 207 (2014) A. Frisk-Kockum et al., Phys. Rev. A, 90, (2014) T. Aref et al., in: Superconducting Devices in Quantum Optics, eds: R.H. Hadfield, G. Johansson (Springer, 2016) arxiv: (2015)

2 The transmon qubit as an artificial atom A capacitively shunted Cooper-pair box f GHz Anharmonicity E C GHz f 12 = 8E J E C 2E C h Φ 0 f 01 = 8E J E C E C h Atom frequency is flux tunable α = h( f 12 f 01 ) E C H = 4E C (n n g ) 2 E J cos( π Φ Φ 0 ) cosθ E C = e2 2C, n = Q 2e, n g = C V g g 2e Jens Koch et al. PRA (2007)

3 Surface Acoustic Waves (SAW) SAW exist at different length scales, from earthquakes to filters in cell phones Exited either mechanically or electrically using the piezoelectric effect Confined to the surface within approximately λ GHz frequencies mk temperatures!ω >> k B T Very low powers ~ -130 dbm Rayleigh, Proc. London Math. Soc., 1885 Animation by L. Braile

4 Generating and detecting SAW with an IDT Piezoelectric substrate (GaAs) Propagation speed: v 3000 m/s Generator and receiver: The Interdigital Transducer (IDT) Datta, Surface Acoustic Wave devices, 1986 Morgan, Surface acoustic wave filters, 2007

5 Circuit model for the IDT Conversion from SAW to current Conversion to SAW Admittance Finger capacitance Resonance when Ba compensates the capacitive term completely

6 Scattering phonons on a qubit Making a transmon into an IDT would allow the qubit to pick up the SAW We should see the same non-linear behavior as with photons Sender IDT Transmon Qubit

7 Interfacing SAW waves with a qubit We have three different controls SAW wave, Gate signal, Flux tuning GaAs Aluminum Gold GaAs v=2900 m/s T = 20 mk, f=4.8 GHz Martin Gustafsson Thomas Aref Maria Ekström

8 The Inter Digital Transducer (IDT) Aluminum on GaAs IDT width = 25 µm N IDT = 125 Finger spacing=λ/2=300 nm v=2900 m/s => GHz Morgan, Surface acoustic wave filters, (2007) Datta, Surface Acoustic Wave devices, (1986)

9 Scattering matrix for the IDT 1 S 21 =S 12 S = Scattering matrix for the IDT Only 4 independent matrix elements S 1 11 S 21 S 21 S 21 S 22 S 32 A S 21 S 32 S 22 S 11 With the qubit detuned we see only the reflection from the IDT => S 11 3 S 33 S 22 2 f IDT = GHz S 11 = 0.50

10 The SAW transmon With the capacitance C shaped into a finger structure, the qubit couples to SAW! The coupling rate can be estimated to be Γ 2π 0.45 N K 2 f Qubit 30 MHz N=20 The number of finger pairs K 2 =0.07% The electromechanical coupling coefficient for GaAs x x+λ/2 Mechanical reflections cancel! SQUID

11 Three types of measurements Reflection Listening Two-tone spectroscopy Acoustic in Acoustic out Electric in Acoustic out Electric + Acoustic in Acoustic out

12 Reflecting a signal off the IDT R [db] f [GHz] S21 2 R = S 11 S i! e i2 L In the fit we have neglected pure dephasing Only electric reflection Reflection vs. flux Electric and acoustic reflection

13 Acoustic reflection on the qubit 38 (R-S 11 ) peak R-S 11 (R-S 11 ) peak

14 Comparing phonons and photons Reflection phonons A) Transmission photons VR Vin 320 um Γ = 38 MHz 2π Γ = 74 MHz 10um 2π (R-S11)peak C) R T 1 0 T P Gustafsson et al., Science (2014) Hoi et al., PRL (2013)

15 Listening to the phonon relaxation Experiment, listening and pumping at GHz Sweeping the flux and the control amplitude -95 3> Gate Power (dbm) Colors represent phonon signal coming out from the IDT photon 2-photon 3-photon Qubit detuning (GHz) f 02 /2 f 02 /2 f 12 f 01

16 Experiment Comparing to theory Listening at GHz Theory Gate Power (dbm) Gate Power (dbm) Qubit detuning (GHz) Qubit detuning (GHz) Fit with Γ = 38 MHz and no pure dephasing

17 Two-tone spectroscopy Reflection coefficient vs. flux and control frequency Exciting f 01 and listening to f 01 f 01 =4.8 GHz f 01 f 12 Exciting f 01 and listening to f 02 f 12 =4.8 GHz f 01 =5.02 GHz Exciting f 12 listening to f 01 f 12 =4.58 GHz Anharmonicity 220 MHz

18 Two-tone spectroscopy for different power comparing experiment and theory Experiment Theory Theory including 6 qubit levels

19 1.5 Time domain experiments, pulse to gate Qubit detuned only cross talk Qubit on resonance, in phase with cross talk Qubit on resonance, out of phase with cross talk 1.0 Vout t H sl S 22 =0.54 Time of flight approximately 40 ns This proves that we are measuring the acoustic response

20 25 ns pulse sent to the gate Time of flight = 40 ns Crosstalk Lightning Vout First SAW pulse Thunder 40 ns Triple transit 80 ns 80 ns 5 times transit Time s

21 Strong coupling possible SAW on LiNbO 3 Piezoelectric coupling to phonons may allow much stronger coupling than is possible with photons Γ 2π 0.45 N K 2 f Qubit 2 K GaAs 2 K LiNbO = 0.07%, N = MHz 5%, N = 40 5 GHz Larger bandwidth Stronger coupling gives impedance matching with fewer fingers, and thus wider bandwidth for the IDTs Optical properties LiNbO 3 exhibits electro-optic effect, Pockel s effect Deep ultrastrong coupling

22 Measurement set up We can measure Reflection Left Reflection Right Transmission left to right Transmission right to left Transmission gate to right Transmission gate to left Thomas Aref Maria Ekström 200 µm 300 µm Measurements at 10 mk

23 Other ongoing experiments Advertising posters

24 Making a single phonon generator Transmon Qubit Josephson junctions Qubit Measurements in progress Measuring correlations from the two sides could prove antibunching Excitation with microwaves π-pulse

25 Optimizing phonon to photon conversion Maria Ekström see poster Characterized at 10 mk 22 db directivity per UDT P.V. Wright IEEE (1985) Morgan, IEEE, (1999)

26 Large atoms, nonexponential decay A two legged atom should have a nonexponential decay See poster by Gustav Andersson When the time of flight between the leggs is large compared to the decay time, interesting things happens Theory: Lingzhen Guo, Anton Frisk Kockum, Göran Johanssson Experiment: Gustav Andersson

27 Summary Nonlinear reflection of phonons from a transmon qubit. Listening to emitted phonons Two tone spectroscopy Strong and controllable coupling on LiNbO 3 Large Lamb shift observed on LiNbO 3 M.V. Gustafsson et al., Science 346, 207 (2014) A. Frisk-Kockum et al., Phys. Rev. A, 90, (2014) T. Aref et al., (Springer, 2016) Experiment Theory Martin Gustafsson Thomas Aref Maria Ekström Gustav Andersson Bala Suri Göran Johansson Anton Frisk-Kockum