Post on 24-Feb-2016
description
Superinductor with Tunable Non-Linearity
M.E. Gershenson
M.T. Bell, I.A. Sadovskyy, L.B. Ioffe, and A.Yu. Kitaev*
Department of Physics and Astronomy, Rutgers University, Piscataway NJ
* Caltech, Institute for Quantum Information, Pasadena CA
Outline:
Superinductor: why do we need it?
Our Implementation of the superinductor
Microwave Spectroscopy and Rabi oscillations
Potential Applications
- A new fully tunable platform for the study of quantum phase transitions?
Impedance controls the scale of zero-point motion in quantum
circuits:
- reduction of the sensitivity of Josephson qubits to the charge noise,
- Implementation of fault tolerant computation based on pairs of Cooper pairs and pairs of flux quanta (Kitaev, Ioffe),
- ac isolation of the Josephson junctions in the electrical current standards based on Bloch oscillations.
Superinductor:dissipationless inductor
Z >> No extra dephasing
Potential applications:
Why Superinductors?
Conventional “Geometric” Inductors
𝑍=𝜔𝐿≈√ 𝜇0
𝜀0=8𝛼×𝑅𝑄 0.4 𝑘Ω
the fine structure constant2
0
1 12 137
ehc
Geometrical inductance of a wire: ~ 1 pH/m.
Hence, it is difficult to make a large (1 H 6 k
@ 1 GHz) L in a planar geometry.
Moreover, a wire loop possesses not only geometrical
inductance, but also a parasitic capacitance, and its microwave
impedance is limited:
Tunable Nonlinear Superinductor
𝐿𝐾ቆ𝑑2𝐸𝐽ሺ𝜑ሻ𝑑𝜑2 ቇ
−1
Δ𝜙=2𝜋 ΦΦ0Φ0≡
h2𝑒 ≈20𝐺 ∙𝜇𝑚2
For the optimal EJL/EJS, the energy becomes “flat” at =1/20.
- diverges, the phase fluctuations are maximized.
Josephson energy of a two cell device (classical approx., )
𝒓 ≡ 𝑬 𝑱𝑳
𝑬 𝑱𝑺
Unit cell of the tested devices: asymmetric dc SQUID threaded by
the flux .
𝐸𝐽= −5× 𝐸𝐽2𝑐𝑜𝑠ቀ𝜑5ቁ−𝐸𝐽1𝑐𝑜𝑠ቀ2𝜋ΦΦ0 −3𝜑5ቁ−𝐸𝐽1𝑐𝑜𝑠ቀ2𝜋ΦΦ0 +3𝜑5ቁ.
Kinetic InductanceThis limitation does not apply to superconductors whose kinetic inductance
is associated with the inertia of the Cooper pair condensate.
Manucharyan et at., Science 326, 113 (2009).
Long chains of ultra-small Josephson junctions:
(up to 0.3 H)
Nanoscale superconducting wires:
InOx films, d=35nm, R~3 k, L~4 nH Astafiev et al., Nature 484, 355 (2012).
NbN films, d=5nm, R~0.9 k, L~1 nH Annunziata et al., Nanotechnology 21, 445202 (2010).
𝐸 𝐽=h
8𝑒2∆𝑅𝑁
=( Φ0
2𝜋 )2 1𝐿𝐾
𝐿𝐾=( Φ0
2𝜋 )2 1𝐸 𝐽
=ℏ𝑅𝑠𝑞
𝜋∆
Tunable Nonlinear Superinductor (cont’d)
I cell2 cells
4 cells6 cells
𝒓𝐨≡( 𝑬 𝑱𝑳
𝑬 𝑱𝑺 )𝒐𝒑𝒕Optimal depends on the ladder length.
two-wellpotential
Inductance Measurements
CK
LC
LC
LC- resonatorinductor
resonatorLK
Two coupled (via LC) resonators:- decoupling from the MW
feedline- two-tone measurements with
the LC resonance frequency within the 3-10 GHz setup bandwidth.
𝜔𝐿𝐶
2𝜋 ≈6−7𝐺𝐻𝑧𝜔𝐾
2𝜋 ≈1−20𝐺𝐻𝑧
1-11
GH
z 3-
14 G
Hz
MW feedline
Dev1Dev2
Dev3Dev4
Multiplexing: several devices
with systematically varied parameters.
“Manhattan pattern” nanolithography
Multi-angle deposition
of Al
On-chip Circuitry
Devices with 6 unit cells
Device
𝐸𝐽𝑆, K
𝐸𝐶𝑆, K
𝐸𝐽𝐿, K
𝐸𝐶𝐿, K 𝑟≡ 𝐸𝐽𝐿𝐸𝐽𝑆
𝐿𝐾ሺΦ = 0ሻ, nH
𝐿𝐾ሺΦ = Φ0/2ሻ, nH
1 3.5 0.46 15 0.15 4.3 3.7 150
2 3.5 0.46 14.3 0.15 4.1 3.8 310
Hamiltonian diagonalization
𝑟 o (𝑁=6 )=(𝐸 𝐽𝐿
𝐸 𝐽𝑆)opt ≈4.1 - for the ladders with six unit cells
4.5
4.3
𝑟 o
𝑟
Rabi Oscillationsa non-linear quantum system in the presence of an resonance driving field.
1
The non-linear superinductor shunted by
a capacitor represents a Qubit.
Damping of Rabi oscillations is due to the
decay (coupling to the LC resonator and the feedline).
Mechanisms of Decoherence
Decoherence due to Aharonov-Casher effect:
fluctuations of offset charges on the islands + phase slips. The phase slip
rate
is negligible (for the junctions in the ladder backbone ).
exp (−𝑐√ 𝐸 JL
𝐸CL) 𝑐≅ 2.5−2.8
𝐸 JL
𝐸CL(≅ 100)
Decoherence due to the flux noise:
Because the curvature (which controls the position of energy levels) has a
minimum at full frustration, one expects that the flux noise does not affect
the qubit in the linear order.
Ladders with 24 unit cells
𝐿𝐾 (𝛷=𝛷0/2 )=3𝜇𝐻almost linear inductor
~ 100m
𝑟 ≈5.2𝑟o (𝑁=24 )≈ 4.5
two-wellpotential
Ladders with 24 unit cells (cont’d)
Number of unit cells
, K , K , K
, KfF nH
, nH , nH
24 3.15 0.46 14.5 0.15 4.6 5 0.8 16 3 000
𝑟 ≈ 4.6𝑟o (𝑁=24 )=(𝐸 𝐽𝐿
𝐸 𝐽𝑆)opt≈ 4.5𝑵=𝟐𝟒
Ladders with 24 unit cells (cont’d)
𝑳𝑲 (𝜱=𝜱𝟎 /𝟐 )=𝟑𝝁𝑯- this is the inductance of a 3-
meter-long wire!
𝑍 (3𝐺𝐻𝑧 )=50 𝑘Ω>𝑅𝑄≡h
(2𝑒 )2
quasi-classical modeling
Double-well potential
𝑟 ≈ 4.2𝑟 o (𝑁=24 )≈ 4.5
Φ=Φ
0
2
crit.
poi
nt
A new fully tunable platform for the study of quantum phase transitions?
Summary
Our Implementation of the superinductor
Microwave Spectroscopy and Rabi oscillations
- Rabi time up to 1.4 s, limited by the decay
Potential Applications
- Quantum Computing
- Current standards
- Quantum transitions in 1D
𝑳𝑲 𝐮𝐩𝐭𝐨𝟑𝝁𝑯