Normal metal - superconductor tunnel junctions as kT and e pumps Jukka Pekola Low Temperature Laboratory, Helsinki University of Technology Coulomb blockade and electronic refrigeration Radiofrequency single-electron refrigerator Heat transistor Hybrid single-electron turnstile for electrons Collaborators: M. Meschke, O.-P. Saira, A. Savin, M. Möttönen, J. Vartiainen, A. Timofeev, M. Helle, N. Kopnin (LTL), A. Kemppinen (Mikes) F. Giazotto (SNS Pisa), D. Averin (SUNY Stony Brook), F. Hekking (CNRS Grenoble)

Principle of electronic refrigeration Conductor 2 T2 Q + W W Q Conductor 1 T1 Q0 Environment Tbath

SINIS in the absence of Coulomb effects M. Leivo, J.P. and D. Averin, 1996

Single electron transistor (SET) Charging energy of a SET: Unit of charging energy:

NIS single-electron box = single-electron refrigerator (SER) J. P. , F. Giazotto, O.-P. Saira, PRL 98, 037201 (2007)

Typical cooling cycle

Quantitative performance of SER Frequency dependence of cooling power Charge and heat flux under typical operation conditions Influence of photon assisted tunnelling: N. Kopnin et al., Phys. Rev. B 77, 104517 (2008)

Heat transistor – Combining Coulomb blockade and electronic refrigeration VDS S N S MAXIMUM COOLING POWER CgVg = (n+1/2)e VDS S N S MINIMUM COOLING POWER CgVg = ne

Influence of charging energy The first demonstration of gate controlled refrigeration O.-P.Saira et al., PRL 99, 027203 (2007) NS contacts

Measured performance of a heat transistor

Brownian refrigerator COOLING POWER OF N (fW) J.P. and F. Hekking, PRL 98, 210604 (2007); see poster by Andrey Timofeev today

Electron pumps Towards frequency-to- current conversion Semiconductor, travelling wave: J.Shilton et al., J. Phys. Condens. Matter 8, L531 (1996) M. Blumenthal, S. Giblin et al., Nature Physics 3, 343 (2007) Fast, but needs still improvement R-pumps: S. Lotkhov et al. Fully superconducting pumps: Fast, hard (but not impossible!) to make accurate Normal single-electron pump: I =ef M. W. Keller et al., APL 69, 1804 (1996). High accuracy but still slow: I < 10 pA

Metrological ”Quantum Triangle” ?

Hybrid single-electron turnstile (SINIS or NISIN) J.P. Pekola, J.J. Vartiainen, M. Möttönen, O.-P. Saira, M. Meschke, and D.V. Averin, Nature Physics 4, 120 (2008)

Stability diagrams Hybrid SET (SINIS or NISIN) Normal SET Important qualitative difference: stability regions overlap in a hybrid SET unlike in a normal SET

Operation cycle Basic operation cycle Exactly one electron is transferred through the turnstile in each cycle: I = ef.

Expected behaviour based on ”classical” tunnelling BLACK – HYBRID SET RED – NORMAL SET Parameters chosen to correspond to the experiment to be presented. DC gate positions are 0, 0.1e, 0.2e, 0.3e and 0.4e (hybrid)

Dependences from the measurement f = 12.5 MHz f = 20 MHz

Bias and frequency dependence of the turnstile current Parameters of the turnstile: RT = 350 kW EC = 2 K

Low leakage NIS junctions IMPROVED JUNCTIONS: A. Kemppinen et al., arXiv:0803.1563 g = 10-5 g = 10-6 THE FIRST EXPERIMENTS, g > 10-4

Error rates (1) Probability (per cycle) of tunnelling in wrong direction is approximately Probability (per cycle) of tunnelling an extra electron in forward direction is approximately Optimum operation point is therefore at eV = D, where the error rate is At typical temperatures (< 100 mK), with aluminium, this error is << 10-8

Error rates (2) Missed tunnelling events due to high frequency: D = EC assumed above. Frequency cut-off can be compensated by parallelisation: compared to N-pump, N parallel turnstiles yield N2 higher current (with the same level of complexity)

Errors in rectangular drive backward tunnelling Parameters: Red D/kT = 20 Green D/kT = 30 Black D/kT = 40 RT = 50 kW f = 300 MHz missed tunnelling

Error rates (3) Possible overheating of the island: The island can cool also!

Error rates: quantum tunnelling Higher order tunnelling processes: In NISIN elastic virtual processes are harmful In SINIS these do not contribute Influence of various inelastic processes?

Error rates (4) Threshold: eV = 2D INELASTIC COTUNNELLING OF QUASIPARTICLES IN A SYMMETRIC SINIS STRUCTURE IS EFFICIENTLY SUPPRESSED eV D S N S Threshold: eV = 2D

Two-electron process and Cooper pair – electron cotunnelling D. Averin and J. Pekola, arXiv:0802.1364 METROLOGICAL REQUIREMENTS SATISFIED IN THEORY

Summary Refrigeration by hybrid tunnel junctions is already a well-established technique as such - Interplay of energy filtering and Coulomb blockade leads to new phenomena and devices Presented a cyclic electron refrigerator, a heat transistor and a Brownian refrigerator Hybrid SINIS turnstile looks promising Simple design and operation Errors can be suppressed efficiently Seems straightforward to run many turnstiles in parallel Possibility for error counting and correction