Radiofrequency singleelectron transistor RFSET as a fast charge

Radio-frequency single-electron transistor (RFSET) as a fast charge and position sensor 11/01/2005

Single-Electron Transistor I q, offset charge DI V q=ne q=(n-1/2)e I and RSET sensitive to offset charge q SET as charge sensor I island charge is quantized when: and k. BT<< e 2/C n=-1 n=0 n=1 q

Limitations of SET Bandwidth Ideal circuit: R, C Intrinsic time scale: output Cc V Ccable D U T Achievable bandwidth in a typical DC setup: Noise-limited bandwidth:

RF-SET as a Fast Electrometer radio-frequency single-electron transistor vr Z = 50 Ω 0 L R, C Capacitance now part of the characteristic impedance! inductor L, SET pad stray capacitance Cp, SET differential resistance Rd(q) form resonant tank circuit Cc Cp D U T V(w 0 t) LCR tank circuit reflected voltage vr changes in charge modulates the amplitude of the reflected signal t Dq(wmt)->DR(wmt) vout q 1 q 0 t Schoelkopf, Science, 280, 1238 (1998) Signal at wm detected after demodulation

Characterization of RF-SET sine wave modulation applied to the gate Frequency domain Demodulated: 0. 05 e offset excitation -40 signal (m. V) 20 15 10 5 0 99. 9 100. 0 frequency (k. Hz) 100. 1 -60 Time domain 0. 05 e offset exictation -80 1. 0909 1. 0910 f(GHz) 1. 0911 0. 10 0. 09 0 Lu, Nature, 422, 423 (2003) 10 20 BW=1 MHz 30 t ( m. S) 40 50 60

Experimental Set-up RF circuit: 1. 0 GHz carrier w 0 N +1 vr T = 4 K to 1. 5 K HEMT circulator amplifier Ga. As FET amplifier directional coupler L Cp reflected voltage mixer Bipolar amplifier w 0 SET N t To digital oscilloscope LO QD Cc Tmix =50 m. K N vout + – N +1 N N t Vbias after mixer

RF-SET coupled to QD depletion gates top view side view Al tunnel junctions Al Al. Ga. As Cc QD QD tunable by gate voltage, capacitively coupled to SET: Excellent electrometer Charge detector QD: Tunable, flexible Coulomb blockade nanostructure System

Real time detection of individual electrons Number of tunneling events a direct measure of the tunneling rate G relatively open dot relatively closed dot

Charge Occupation probability two level system near a charge degeneracy point dot switching between two charge states: Can directly measure the occupation probability of the N electron charge state

Distribution Function charge occupation probabilities: Distribution function: Thermally broadened Fermi distribution Tunneling rate directly measured Lu, Nature, 422, 423 (2003)

RF-SET as fast charge sensor Can see transition rate pick up as QD source/drain bias is increased. Can also monitor charge fluctuations. In principle, can acquire complete statistical information about current flow! Great potential applications for quantum computation, for example. Lu, Nature, 422, 423 (2003)

RF-SET as displacement sensor RF-SET Q 0=Cg. Vg DQ 0=Vg. DCg Vg. Dd resonator Apply fixed voltage Vg to the beam, and the RFSET output measures the beam’s motion (changes in d) La. Haye, Science, 304, 74 (2004) d SET Mechanical resonator

RF-SET as displacement sensor La. Haye, Science, 304, 74 (2004) Ultrasensitive displacement detection achieved Detect the properties of the resonator by simply “listening”, without driving it (a factor of 4. 3 away from the quantum limit)

High BW particle/cell counter Wood, APL, 87, 184106 (2005) RF reflectance data taken for flowing 15 mm beads through the microfluid channel Problems associated with large R, Cs solved by the RF resonant circuit BW>10 MHz Millions of beads (cells) can be counted per second