To Quantum Dots and Qubits with electrons on helium

To Quantum Dots and Qubits with electrons on helium CEA-DRECAM Service de Physique de l Etat Condensé CEA-Saclay France E. Rousseau D. Ponarine Y. Mukharsky E.Varoquaux O. Avenel J.M. Richomme

Confine the electrons Guard electrode the exact quantity of helium is added to fill the two pools and the ring. L pool R pool ring electrons are created by a corona discharge. Only electrons above pools and ring are mobile. 550 nm pool Guard electrode 40 nm

trapping R pool Gate -V (Volt) SET=0.1 SET=0.2 X axis R pool SET=0.35 Gate The electrostatic trap is created by the SET itself.

Royal holloway Sample more or less similar to RHL one. Counting Individual Electrons on liquid Helium. G.Papageorgiou & al. Applied physics letters 86, 153106 (2005)

Sample specificity: The Precious Ring diameter 3 μm, pyramidal SET island Guard electrode L pool R pool ring

Gate ResR

Detection ResR Q+ q SET island SET oscillations amplitude The voltage across the SET is a periodic function of the island charge. When an electron goes in or out of the trap the SET island charge change by dq. Re()sRCVfe Re()sRCVqfee +

Detection SET oscillations amplitude oscillations phase We fit with a spline function a quiet part of the oscillations. The phase of the oscillations changes then by df.

Charging the ring Drawing of the potential profile guard guard Left and right pools ring

One by one observation -92 phase Q/e -94-96 -98 ResR SET -100 0.0 0.3 0.6 0.9 1.2 Right pool potential, V

One by one observation -92.0-92.5 0.4e -93.0 0.4e -93.5 Q/e -94.0-94.5-95.0 0.6 0.7 0.8 0.9 1.0 ResR last jumps are around ~0.4 e, value which is reproduced by simulations.

phase variation Discharge curve Zoom

phase variation Discharge curve

phase variation Discharge curve 1 2 3 q 4 5 6 8 9 0

SET island charge Q/e Discharge curve

Density estimate Electron sheet R h S eff max SET island For a small number of electrons, density can be considered as uniform. A.A.Koulakov, B.I.Shklovskii condmat/9705030 The electric field is supposed to be constant on SET island. The electric charge on the SET island is then given by: Q ns eff (1-cos( max )) e = 2 0 With max =arctan ( 1 N h n ) N=n R 2 number of electron n electronic density

Density estimate Electronic density=(1.8 +/- 0.4) 10 14 m -2 SET island charge Q/e S eff =0.34 +/- 0.07 μm 2 S real =0.35 μm 2

The interaction between electrons is not screened by surrounding electrodes. From thermal fluctuations: n=10 14 transition temperature Tc=2.5 K r s ~2000 r s cri ~30 Coulombic interaction is dominant Electrons should form a Wigner crystal.

Wigner molecules Competition between the symmetry of the trap (parabolic trap) Ø shell ordering N=7 and the symmetry of the Wigner crystal Ø triangular lattice structure N=19

macroscopic observation camera No observations with electrons on helium.

Addition Spectra Current pa 20 μ(1) 4 10 μ left gate μ right 1 2 3 Gate voltage, V charging energy: energy required to add one electron μ(n) =μ(n)-μ(n-1) ~ e V g

Addition spectra phase variation μ(3) μ(2) μ(1)

Liquid phase Average interaction between electrons Ø Constant interaction model Ø 1 particles model in a parabolic trap Confinement induce energy shell with magic numbers when a shell is completely filled: 2,6,12 (degeneracy due to spin) 2eC+ 2eC++

Hund s rule

addition energy (ev) For a parabolic trap The numbers of electrons on each ring are not universal and depend on the type and strength of confinement potential. Vladimir Bedanov and François Peeters PRB 49, 2667 B.Partoens and F.Peeters J.Phys:condens matter,9 5383 (1997) No magic numbers when electrons form Wigner molecules. Simulations needed to explain addition energy plot

Pour Vset=0.3 Vgate=0 Vground=-0.1 0.10 0.08 ev 0.06 0.04 0.02 0.00 0 2 4 6 8 10 nombre d'electron

chemical potential variation Vset=Vgate=0.5 V

Monte Carlo simulations The model potential profile found with simulation Ø simulation of the pyramidal island. Ground state of the configuration with N electrons is found with Monte-Carlo Simulations. Ground state energy vary linearly with reservoir right potential.

energy (ev) N=19 N=20 N=21 N=22

Monte Carlo simulations The model potential profile found with simulation Ø simulation of the pyramidal island. Ground state of the configuration with N electrons is found with Monte-Carlo Simulations. Ground state energy vary linearly with reservoir right potential. Criteria when the electron leaves the trap?

potential profile Potential profile = one particule energy One electron leaves the trap when NN

(ev) E 22 -E 21 E 2 -E 1

Vset=0.5 Vgate=0.5 additionenergy(ev) simulation experiment

Addition energy μdot (N) (mev) 4 6 Vset=0.1 Vgate=0.2 9 Clear magic numbers! Cannot be explain with M-C simulation Positive impurity increase locally the density Structural transition in a finite classical two dimensional system G. A. Farias and F. M. Peeters solid state communication, 100, 711 (1996)

One by one observation Q/e -95-100 0.6 0.9 ResR, V

Probability of escape If the barrier is thin enough, the electron can tunnel. barrier height

Quantum state evidence? Potential profile 1> Barrier height probability 0> position

Existing to the first excited state 1> 0> Oscillating E Potential felt by the electron I SET +e -e Tunneling time =5.10-11 s Time mix =75 μs

measurement principles Potentials profiles? Barrier position 1. We choose a SET current value from 0 namp (no heating) to 50 namps. 2. We applied a voltage pulse to the right reservoir: the barrier height is reduce. 3. We check whether the electron is still in the trap or not. 4. 2000-3000 tries for one escape curve.

Temperature estimate p= 1-exp(- 0 exp(-e b /k b T)) probability of extraction 0 = 0 /2 0 /2 ~ 30 GHz trap frequency pulse length E b barrier high E b and 0 estimated from simulations

Curve width with heating current 1.6 1.4 1.2 1.0???? 0.8 0.6 0.4 0.2 0.0 Fit with numerically calculated U Multipler 33.61 v 0 =0.076,? 0 =.0052-30 -20-10 0 10 20 30 The pulse is applied during heating Ids

A0.5 probability of extraction

4.1 4.0 Quantum tunneling Thermal activation A 0.5 3.9 Crossover Temp ~ 250 mk 3.8 3.7 0 200 400 600 800 1000 T, mk

the frequency of the barrier energie (ev) 0 0 ~ 30 GHz (before the pulse) Cross-over temperature 02BhTk : ~ 230 mk

1.0 Vset=0.3 extraction curve probability 0.8 0.6 0.4 0.2 Vsetapp=0.2598 Temp=0.235 K Tcell=30 mk Only one parameter is adjusted Ø Vset. 0.0 0.644 0.646 0.648 0.650 0.652 0.654 ResR potential Contact potential between niobium and aluminium the potential on the SET is not really known

2.9 2.8 2.7 A 0.5 2.6 2.5 2.4 Ids 0 Ids 2.3 Ids 10 Ids 0 Ids 2.3 Ids 10 0 200 400 T, mk 600 800 1000 No change when we heat the electron! Need to probe the coupling between the electron and its environment

SET Potential profile Coupling with environment Barrier position 100 μs 1. Heating for 300 ms with 50 namps. 2. Wait between 2 and 100 μs. 3. Applied the pulse on reservoir right. 4. Fit the curve. According to position and width of this curve get a number proportional to the temperature

Coupling with the environment 2000 t=0 high temperaure Sep07 Sep09 Ekt 4000 Even for t=2 μs, temp. is low. 6000 8000 10000 12000 20000 18000 16000 14000-20 0 20 40 60 80 100120140160180200220240260280300320, μs

Heating pulse decay Heating current 50 namps ~ 0.4 μs time

temperature a-u

temperature a-u tau = 0.38 +/- 0.05 micro-s ttaue

What can we say? Either the coupling with the environment is huge

Where does it come from? Coupling with phonons they induce modulations of the density. So they induce modulation of the image charge. This coupling depends highly with the electric field on the electron. In our case ~ 10 μs We maybe tried the smallest electric field as we could to keep the electron in the trap!

What can we say? Either the coupling with the environment is huge Or the picture of the heating procedure is too naïve Dynamical force? 1> 0> I SET

Two wave-guids: ~ 40 GHz Ø parrallel levels ~ 120 GHz Ø perpendicular levels

(ev)

Evolution with deformation ellipsoïdal Increase of the deformation circular

Bias and IV characteristic L pool Guard electrode R pool I ds ring A U ds PreAmp A-B B the SET is current bias

IV Characteristic 6.0x10-4 4.0x10-4 500 mk sample 2h UDS, V 2.0x10-4 For C-B oscillations 0.0-2.0x10-4 -4.0x10-4 -6.0x10-4 -8.0x10-4 -5-4 -3-2 -1 0 IDS, na 1 2 3 4

Measurement L-in technique: 125 Hz, 6-30 μv applied to the guard Guard electrode PreAmp L pool 6 μv R pool ring L-in 125 From L-in

C-B oscillations Amplitude C-B oscillations Amplitude C-B oscillations Raw oscillations From L-in I ds =2.6 na

Some properties of this kind of quantum dots Classical point of view: competition between thermal fluctuations and coulombian interaction for n=10 14 transition temperature Tc=2.5 K Working temperature: from 50 mk to 1K

Gas parameter Measure the competition between quantum fluctuations and Coulombic interaction For n ~ 10 14 m -2 a ~n -1/2 ~ 0.1 μm a typical coulomb energy Typical kinetic energy (Fermi energy) rs~2000 rs cri ~30 Coulombic interaction is dominant Semiconductors qdots rs~2 2014ceEa : 22KEmah:

chemical potential variation Vset=Vgate=0.3 V 5 7