Developing Quantum Logic Gates: Spin-Resonance-Transistors

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Donald Blair
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1 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

2 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

3 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

4 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

* initializations long term cryogenic solutions for military

5 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

6 First-stage experiments: * to electrically detect electron-spinresonance (ESR) of few spins (conventional ESR requires 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

7 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

8 13 GHz, 15 dbm 1.3 K, 0.5 T/min Hz, 10 mv 3 msec 0.12 I (90 o ) I (0 o ) 4 3 capacitance and resistance % modulation, 8.8 Hz 1 Sec/1 Sec 4 di (90 o ) di (0 o ) B (T) B (T) 3 2 changes of capacitance and resistance due to microwave radiation (nonresonant)!ω c gµ B B a spin-1/2 system at odd filling factors E=(N+1/2)!ω c +gµ B B

9 * detected ESR in different samples with spins * line-width 50 MHz (for field scan-up) * also detected in capacitance (spin-flip change DOS)

10 2.5 2DEG in a Waveguide sweep-up sweep-down 14.8 GHz 15.0 GHz T = 1.3 K dr xx (Ω) GHz 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

11 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 Al 0.3 Ga 0.7 As Ψ(Ζ) GaAs g = +0.4 g = Vg = 0 Vg> 0 g eff = g ( z ) ψ ( z ) 2 dz ψ ( z ) = f ( V g )

12 dr xx dr xx dr xx dr xx dr xx V V ESR spectra at different gate-voltages f = 15.2 GHz, T =1.2 K V V V Magnetic Field (T)

13 g-factor Gate-Voltage (V)

14 Next: 1. ESR detection with small FET ( electrons in the channel) Structures have been fabricated in UCLA Nano-Structure Research Lab. for the experiments

15 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 ) GHz (20 dbm) 1.25 K ESR dr xx with microwave amplitude modulation R xx direct resistive detection ESR Magnetic Field (T) * ESR can be detected with large microwave power

16 A resonant cavity is being fabricated

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