Non-equilibrium superconductivity in microwave resonators

Transcription

1 Non-equilibrium superconductivity in microwave resonators Cooper Pairs 2Δ hν Pieter de Visser Quasipar/cles SRON: Stephen Yates, Jochem Baselmans, Pascale Diener, Andrey Baryshev Delft: Teun Klapwijk, Nuria Llombart, Andrea Neto Cambridge: Tejas Guruswamy, David Goldie, Stafford Withington Moscow: Sasha Semenov, Igor Devyatov Superconductivity and Photons

2 From light to signal Cooper Pairs 2Δ hν Quasipar/cles S21 [db] δf F 0 Incoming photons break Cooper pairs => quasipar/cles => Higher resistance and inductance => Resonance shi@s and gets shallower Microwave readout, energies far below the gap F [Ghz] P. Day, et al., Nature 425, 817 (2003)

3 From light to signal Cooper Pairs 2Δ hν Quasipar/cles Microwave: Q i, A Pair breaking Microwave: f res, θ

4 Nonequilibrium Absorp/on: - Cooper pair breaking by photons - Microwave absorp/on by quasipar/cles Field effect: - Density of states broadens due to field => nonlinearity Removing nonequilibrium QP s with trap/sink tricks does not work for detectors, we want to collect them!

5 Nonequilibrium due to absorption Injec/on rate of quasipar/cles at energy E - Microwave - Cooper-Pair breaking

6 Excess quasipar/cles Microwave power dependent Phys. Rev. Lett. 106, (2011) Appl. Phys. Lett. 100, (2012)

7 Influence of microwave dissipa/on on pair-breaking response (1.5 THz) Detector sensitivity limited by excess QPs due to microwave readout We need the microwave power, because we want to be limited by qp-fluctuations Nature Communications 5, 3130 (2014)

8 Influence of microwave dissipa/on on pair-breaking response (1.5 THz) Not limited by stray-light Detector sensitivity limited by excess QPs due to microwave readout Nature Communications 5, 3130 (2014)

9 Non-linear resonator response curves

10 Low T quasipar/cle crea/on, but at higher T Q i enhancement

11 Non-equilibrium f(e) Ivlev, Lisitsyn, Eliashberg, JLPT 10, 449 (1973) - Microwave absorption, gap enhancement close to Tc Chang and Scalapino, PRB 15, 2651 (1977) - kinetic equations Goldie and Withington, SuST 26, (2013) low temperature, resonators

12 Non-equilibrium f(e) Ivlev, Lisitsyn, Eliashberg, JLPT 10, 449 (1973) - Microwave absorption, gap enhancement close to Tc Chang and Scalapino, PRB 15, 2651 (1977) - kinetic equations Goldie and Withington, SuST 26, (2013) low temperature, resonators

13 Non-equilibrium f(e) steady state Goldie and Withington, SuST 26, (2013) Phys. Rev. Lett. 112, (2014)

14 Phys. Rev. Lett. 112, (2014) Example f(e) -> σ 1, Q i

15 Nonequilibrium due to absorption Injec/on rate of quasipar/cles at energy E - Microwave - Cooper-Pair breaking

16 Efficiency in converting photon energy to QPs close to the gap Phonon trapping factor Guruswamy, Goldie, Withington, SuST 27, (2014) Arises because observable is mainly sensitive to quasiparticles close to gap

17 Broadband antenna + lens Tantalum KID, energy gap at 324 GHz Absorber detector will not work, due to Z s (ω), constant power needed Neto, IEEE Trans. Antennas and Prop. 58, 2238 (2010) Neto et al. IEEE Trans. THz Sci. Tech. 4, 26 (2013)

18 FTS response of Tantalum resonator 1 Absorption measurement, Detector phase response (a.u.) Δ 4 Δ resonator is detector in FTS FTS dependence (calibrated) Antenna efficiency Absorption superconductor Frequency (GHz) Response superconductor

19 CPW absorption x antenna efficiency Detector phase response (a.u.) Energy gap Ta: 324 GHz Frequency (GHz)

20 Constant power, only effect is F-dependence through f(e) Steady state f(e) Non-equilibrium quasiparticle distribution

21 Steady state f(e) Non-equilibrium quasiparticle distribution QP creation efficiency Constant power, only effect is F-dependence through f(e) Frequency (GHz)

22 We measured pair-breaking efficiency due to f(e,f) Appl. Phys. Lett. 106, (2015)

23 Monochromatic pair-breaking illumination (high energy) Microwave power dependence consistent with our observations Phys. Rev. B 93, (2016) R. P. Budoyo, PhD Thesis (2015)

24 Absorp/on does not explain everything

25 One level deeper Absorp/on is only part of the non-equilibrium story of a superconductor in an AC field. Vector poten/al A, pulls apart the pair in momentum space - In equilibrium the two electrons have opposite momenta: k 1 +k 2 =0. - In a DC-field this becomes k 1 +k 2 =q => density of states broadening => nonlinear L

26 DC Anthore et al. PRL 90, (2003) Eom et al. Nature Phys. 8, (2012) Density of states broadens, but gap remains hard. Inductance shows an I 2 non-linearity => used to model (RF!) travelling wave parametric amplifier

27 DC Anthore et al. PRL 90, (2003) Eom et al. Nature Phys. 8, (2012) Density of states broadens, but gap remains hard. Inductance shows an I 2 non-linearity => used to model (RF!) travelling wave parametric amplifier

28 One level deeper Absorp/on is only part of the influence of the field on the superconductor, through f(e). Vector poten/al Acos(ωt), pulls apart the pair in momentum space - In equilibrium the two electrons have opposite momenta: k 1 +k 2 =0. - In a DC-field this becomes k 1 +k 2 =q => density of states broadening => nonlinear L - For finite frequency: k 1 +k 2 =q 0 cos(ωt), now it depends on the frequency and field strength NOTE: the momentum effect is also known as depairing or pair-breaking, but it is NOT the same as pair-breaking due to a photon/phonon with E>2Δ

29 Microwave: Coherent excited states Superconducting state (density of states) changes drastically 2 differences compared to DC: Steps at multiples of hf Exponential subgap tail triggers absorption? Semenov, Devyatov, de Visser, Klapwijk, arxiv: Much richer structure than DC

30 Effect on complex conductivity Nonlinear frequency-shift for Al resonator that is not due to f(e) effect, is quantitatively explained! But needs other type of experiments to fully explore the density of states. Semenov, Devyatov, de Visser, Klapwijk, arxiv:

31 Summary Phys. Rev. Lett. 112, (2014) Nature Comm. 5, 3130 (2014) Appl. Phys. Lett. 106, (2015) arxiv: Current direction: move to much smaller detection volumes => nonlinear, single quasiparticle