Developing Quantum Logic Gates: Spin-Resonance-Transistors H. W. Jiang (UCLA) SRT: a Field Effect Transistor in which the channel resistance monitors electron spin resonance, and the resonance frequency is in turn controlled by the gate voltage. gates FET charge sensors
Single qubit operations σ x α and σ z α * Each SRT can be tuned, individually, in and out resonance with the global microwave field by the gate-voltage * arbitrary rotations can be performed by varying the gate pulse width at electron-spin-resonance ex: π/2 pulse ( t= π/2γb AC ) B * = B AC i * the spin process about this field at a rate Ω= γb AC µ B=d J/dt in a rotating coordinate frame: B * =B AC i * +(B DC -ω/γ)k * ω 0 = γb DC
Two-qubits operations Swap -S α two-qubits Wavefunction entanglement Triplet states 4 J ( r ) h 1.6 q εa 2 B r a B 5 / 2 2 r exp, a B Singlet state * J-exchange interaction depends on the overlap of the wavefunctions which is controlled by gate voltages * At off-resonance, the wavefunction can be controlled by gate voltages as the gate pull the electron away from the nucleus: Coulomb potential is weakened a B increases J-exchange overlap turns on
To implement a CNOT gates: σ x -1/2 S 1/2 S 1/2 σ x σ z 1/2 σ x 1/2 σ z 1/2 A precise electrical control of the ESR (the resonance frequency and the pulse timing) is need
Environment for the devices:1.2 K, 2-3 T Field and temperature considerations: * long T 2 * initializations long term cryogenic solutions for military applications: * use compact close-cycle refrigerator * use small high-field permanent magnet
First-stage experiments: * to electrically detect electron-spinresonance (ESR) of few spins (conventional ESR requires 10 12 electrons) * to gain control of ESR by gate * to explore the potential of using nuclear spin for quantum memory Using GaAs/AlGaAs heterostructures first: * direct gap material (easy to integrate with single photon emission and detection) * reasonably long relaxation time: T 2 * about 100 ns * clean system: high mobility (10 6 cm 2 /V-Sec, mean-free path of 1-micron) * vast amount of knowledge about the electrons in the quantized magnetic-field from the research of quantum Hall effects
measurements V g source channel AlGaAs GaAs gate lock-in at 520Hz drain Hz I V ac 520 Hz δi microwave modulated at 7 Hz lock-in at 7 Hz gate C R channel tanh α I = V ac { }, α α for ω RC << 1 I ( 0 ) o I (90 ) R C jω RC 1/ C = 1/ C C Q geometric 2 n e ( µ ), + 1/ C n density of states µ Q
13 GHz, 15 dbm 1.3 K, 0.5 T/min 0.06 0.14 520 Hz, 10 mv 3 msec 0.12 I (90 o ) 0.10 0.08 0.06 3 0.04 I (0 o ) 4 3 capacitance and resistance 0.02 0.04 0.02 4 2 0.00 0 1 2 3 4 2 0.00 0 1 2 3 4 0.015 100% modulation, 8.8 Hz 1 Sec/1 Sec 4 di (90 o ) 0.010 0.005 0.000 4 3 2 0.01 di (0 o ) 0.00-0.01 0 1 2 3 4 0 1 2 3 4 B (T) B (T) 3 2 changes of capacitance and resistance due to microwave radiation (nonresonant)!ω c gµ B B 1 1 0 0 a spin-1/2 system at odd filling factors E=(N+1/2)!ω c +gµ B B
* detected ESR in different samples with 10 5-10 10 spins * line-width 50 MHz (for field scan-up) * also detected in capacitance (spin-flip change DOS)
2.5 2DEG in a Waveguide 2.0 1.5 sweep-up sweep-down 14.8 GHz 15.0 GHz T = 1.3 K dr xx (Ω) 1.0 0.5 15.5 GHz 0.0 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 B (T) * Overhauser shift due to the hyperfine interaction # " 1 A I S = A { ( I + S + I S + ) + I z S z } 2 DNP by a mutual flip of electron and nuclear spins * long nuclear relaxation (~ 700 Sec) showing potential for quantum information storage
Gate Controlled ESR (g-factor engineering) ψ(z) 2 V g2 µ evg E 0 V g1 E F NiCr gate GaAs Si-doped AlGaAs undoped Al 0.3 Ga 0.7 As g +0.4 GaAs g -0.44 Al 0.3 Ga 0.7 As Ψ(Ζ) GaAs g = +0.4 g = -0.44 Vg = 0 Vg> 0 g eff = g ( z ) ψ ( z ) 2 dz ψ ( z ) = f ( V g )
dr xx dr xx dr xx dr xx dr xx 0.0006 0.0004 0.0002 0.0003 0.0006-0.336 V 0.0003 0.0006-0.328 V 0.0003 0.0000 ESR spectra at different gate-voltages f = 15.2 GHz, T =1.2 K -0.351 V 0.0000 2.56 2.57 2.58 2.59 2.60 2.61 2.62 0.0009 0.0006-0.343 V 0.0000 2.56 2.57 2.58 2.59 2.60 2.61 2.62 0.0000 2.56 2.57 2.58 2.59 2.60 2.61 2.62-0.0003 2.56 2.57 2.58 2.59 2.60 2.61 2.62 0.0012 0.0010 0.0008-0.321 V 0.0006 0.0004 2.56 2.57 2.58 2.59 2.60 2.61 2.62 Magnetic Field (T)
0.4210 0.4205 g-factor 0.4200 0.4195 0.4190 0.4185-0.355-0.350-0.345-0.340-0.335-0.330-0.325-0.320 Gate-Voltage (V)
Next: 1. ESR detection with small FET (100-1000 electrons in the channel) Structures have been fabricated in UCLA Nano-Structure Research Lab. for the experiments
Next: 2. Time-resolved detection of ESR use high Q-cavity to boost up B ac : (1/(γ B ac )>>T 2, T 1 * eliminate lock-in detectors for detection, make device application practical * do time-resolved ESR (ex. to measure the spin-flip time T 1 ) -0.01 19.5 GHz (20 dbm) 1.25 K ESR dr xx -0.02 with microwave amplitude modulation 0.0000225 3.4 3.5 3.6 3.7 3.8 0.0000200 R xx 0.0000175 0.0000150 direct resistive detection ESR 0.0000125 3.4 3.5 3.6 3.7 3.8 Magnetic Field (T) * ESR can be detected with large microwave power
A resonant cavity is being fabricated