Chalmers University of Technology
Quantum acoustics and
An atom in front of a mirror
Placing artificial atoms
in unusual environments
Ø  Interaction between SAW and a qubit
Ø  Nonlinear reflection
Ø  Listening to a qubit relaxing
Ø  Two tone spectroscopy
Ø  An atom in front of a mirror
M.V. Gustafsson et al., Science 346, 207 (2014)
T. Aref et al., arXiv:1506.01631 (2015)
Ø  Reflecting light from an “atom”
Ø  Placing an “atom” in front of a mirror
Ø  Cancelling vacuum fluctuations
Ø  Summary
I.-C. Hoi et al., Nature Physics 11, 1045 (2015)
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Generating and detecting SAW with an IDT
• 
• 
Piezoelectric substrate (GaAs, quartz,
LiNbO3…)
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
Per Delsing
Quantum Device Physics
Chalmers University of Technology
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
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Interfacing SAW waves with a qubit
GaAs Aluminum Gold
We have three different controls
SAW wave, Gate signal, Flux tuning
Read-out of the acoustic signal
T = 20 mK, f=4.8 GHz
Per Delsing
Quantum Device Physics
Chalmers University of Technology
The Inter Digital Transducer (IDT)
Aluminum on GaAs
IDT width = 25 µm
NIDT = 125
Finger spacing=λ/2=300 nm
v=2900 m/s
=> 4.8066 GHz
Morgan, Surface acoustic wave filters, (2007)
Datta, Surface Acoustic Wave devices, (1986)
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Scattering matrix for the IDT
Scattering matrix for the IDT
Only 4 independent matrix elements
1
0
S11 S21 S21
S = @ S21 S22 S32 A
S21 S32 S22
1
S11
S33
S21=S12
With the qubit detuned we see only
the reflection from the IDT => S11
S22
3
fIDT = 4.8066 GHz
S11= 0.50
2
Per Delsing
Quantum Device Physics
Chalmers University of Technology
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
≈ 0.45 N ⋅ K 2 ⋅ f Qubit ≈ 30 MHz
2π
•  N=20
The number of finger pairs
• 
The electromechanical coupling
coefficient for GaAs
K2=0.07%
∆x
∆x+λ/2
Mechanical
reflections
cancel !
Per Delsing
SQUID
Quantum Device Physics
Chalmers University of Technology
Three types of measurements
Reflection
Listening
Two-tone
spectroscopy
Acoustic in
Acoustic out
Electric in
Acoustic out
Electric + Acoustic in
Acoustic out
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Reflecting a signal off the IDT
6
5
f [GHz]
4
3
2
1
0
-1.0
0.0
0.5
1.0
R [dB]
-0.5
R = S11
⇣
S22 + 1
2
S21
i !
⌘
e
i2✓L
In the fit we have neglected pure dephasing
Only electric
reflection
Electric and acoustic
reflection
Reflection vs. flux
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Acoustic reflection on the qubit
(R-S11)peak
R-S11
(R-S11)peak
38
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Listening to the phonon relaxation
Experiment, listening and pumping at 4.8066 GHz
Sweeping the flux and the control amplitude
|3>
-95
Gate Power (dBm)
-100
-105
-110
-115
-120
-125
Colors represent phonon
signal coming out from
the IDT
f02/2
f02/2
f12
f01
3-photon
2-photon
1-photon
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
Qubit detuning (GHz)
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Comparing to theory
Listening at 4.8066 GHz
Theory
-95
-95
-100
-100
Gate Power (dBm)
Gate Power (dBm)
Experiment
-105
-110
-115
-120
-125
-105
-110
-115
-120
-125
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
Qubit detuning (GHz)
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
Qubit detuning (GHz)
Fit with Γ = 38 MHz and no pure dephasing
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Two-tone spectroscopy
Reflection coefficient vs. flux and control frequency
– f01
– f12
Exciting f01 and listening to f01
Exciting f01 and listening to f02
f12=4.8 GHz
f01=5.02 GHz
f01=4.8 GHz
Exciting f12 listening to f01
f12=4.58 GHz
Anharmonicity ≈ 220 MHz
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Two-tone spectroscopy for different power
comparing experiment and theory
Experiment
Theory
Theory including
6 qubit levels
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Summary I
• 
• 
• 
• 
Nonlinear reflection of phonons from a transmon qubit.
Listening to emitted phonons
Two tone spectroscopy
Pulsed measurements show the acoustic character
M.V. Gustafsson et al., Nature Physics, 8, 338 (2012)
M.V. Gustafsson et al., Science 346, 207 (2014)
A. Frisk-Kockum et al., Phys. Rev. A, 90, 013837 (2014)
T. Aref et al., arXiv:1506.01631 (2015)
Experiment
Martin
Gustafsson
Thomas
Aref
Theory
Maria
Ekström
Per Delsing
Göran
Johansson
Anton
Frisk-Kockum
Quantum Device Physics
Chalmers University of Technology
Placing an atom in front of a mirror
We place an “atom” (or superconducting qubit) on a chip
We limit the electromagnetic field to one dimension
A mirror is made by a thin metallic layer that shorts the electric field.
We use a superconducting short in 1D as a mirror.
Per Delsing
Quantum Device Physics
Chalmers University of Technology
A)
Transmission for a single
“atom” (no mirror)
V
R
Microwaves are sent on resonance
towards the qubit and transmission is
measured
Nonlinear
transmission
Vin
At low power everything is reflected
by the qubit
320 um
At high power everything is transmitted
10um
C)
R
T
1
0
T
100nm
P
Total extinction: 99.6% extinction observed
Shen and Fan, PRL (2005).
Astafiev et al. Science (2010)
Per Delsing
Hoi et al. PRL (2011)
Quantum Device Physics
Chalmers University of Technology
Placing an atom in front of a mirror
Atom-mirror distance L=11 mm
Sample layout
Mode structure for
L=λ/2 and L=3λ/4
We can change the atom frequency, thus effectively
changing the distance to the mirror, i.e. the distance
measured in number of wavelengths.
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Measurement set-up
The atom is placed at the
distance L= 11 mm from the
mirror.
We measure microwave
reflection from the atom/mirror
system
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Doing spectroscopy on the “atom”
Reflection at low power
From the dip we can extract
the relaxation rate Γ1 and
decoherence rate γ
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Reflection from the atom and the mirror
Nonlinear reflection of microwaves off the ”atom”
At low power the microwaves are reflected from the atom.
At high power the microwaves are reflected by the mirror
On resonance
Control experiment for relaxation rate Γ1 and decoherence rate γ
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Doing spectroscopy on the “atom”
Spectroscopy
The ”atom” is invisible around 5.4 GHz
The quantum fluctuation from the transmission
line and from the mirror interfere
Per Delsing
Extracting the relaxation rate
T1 differs by a factor of 10
Quantum Device Physics
Chalmers University of Technology
Measuring the quantum fluctuations
Quantum fluctuations are hard to measure since you cannot extract the energy.
Spontaneous emission of an atom is caused by quantum fluctuations, so
measuring the decay rate, we can indirectly measure the quantum fluctuations.
The quantum fluctuation from the transmission
line and from the mirror interfere
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Measuring the vacuum fluctuations
as a function of the distance to the mirror
Narrow range
Wider range
When the ”atom” is half a wavelength from
the mirror the quantum fluctuations vanish
(only for the atom-frequency)
Probe power corresponds to 0.04 photons
I.-C. Hoi et al., Nature Physics 2015
Per Delsing
Quantum Device Physics
Chalmers University of Technology
Summary II
•  Investigated an atom in front of a mirror
•  The life time of an atom can be modified in front of a mirror
•  Quantum fluctuations can be canceled to extend the life time of atoms
I.-C. Hoi et al., Nature Physics 11, 1045, (2015)
Experiment
IoChun
Hoi
Chris
Wilson
Arsalan
Pourkabirian
Per Delsing
Göran
Johansson
Theory
Lars
Tornberg
Anton
Frisk-Kockum
Quantum Device Physics