Topics on Electrical Manipulation and Detection of Spin Qubit

1. Topics on Electrical Manipulation and Detection of Spin Qubit 2011-3-10 魏达

2. Brief Review • Loss and DiVincenzo Criteria (Guidance of all the efforts) • Scalability • Initialization to Pure State • Qubit Read-out • Long Coherence Time • Universal Quantum Gates • Building blocks are demonstrated feasible • The Criteria are satisfied better and better

3. On Qubit Read-out • Early proposal: magnetically driven ESR & Employing Coulomb blockade in Read out • Technically challenging: • Read out need a high magnetic field (such that Zeeman splitting exceeds thermal broadening) • in ESR, lower magnetic field is more desirable (high external magnetic field lead to high frequency of B_ac, accompanied by undesired E_ac, which will induce destructive PAT effect)

4. Electrically driven spin manipulation has following advantages: • Easier to generate • Capability of being excited locally • Less Ohmic heat on-chip e.g. • experiments exploiting ac electrical field to rotate single electron spin has been demonstrated • SWAP gate, realized by AC electrical controlled interdot exchange interaction.

5. Scalability • Initialization to Pure State • Qubit Read-out • Long Coherence Time • Universal Quantum Gates Vistas • Integrating of read-out, coherent control and SWAP gate in a single experiment, which will enable us to perform CNOT gate Challenging issues like: • Such experiments have to be performed in different regime • Single spin has to be addressed individually • Read-out should be able to distinguish 4 eigenstates Key factor: Read-out Scheme

6. Key Factor: Read-out Scheme • Way I: • Another set of “read-out quantum dots”, i.e., quadruple sample is needed. • Essence: spin-dependent interdot tunneling rate • Way II (theme of the second part): • Employing synchronized double pulses to explore two spin at once

7. Scalability • Initialization to Pure State • Qubit Read-out • Long Coherence Time • Universal Quantum Gates Vistas Dominating decoherence mechanism in GaAs is Hyperfine interaction while spin-orbit coupling only contribute to the relatively slow relaxation processes. • Relaxation rate rather slow ,T1 is about 1s • Randomness of nuclear field dephase spin in about 10-40ns • 70mT echo pulse, 0.5s for a single spin • 100mT echo pulse, 1s for a two-spin state

8. Improving Coherence Time Reducing the randomness of the nuclear field Polarization over 99% will extend dephasing time by an order of magnitude Spin pumping Other materials Si/SiGe and Carbon based material Alternative encoding of the logical qubit Singlet/Triplet encoding Higher magnetic field Use higher magnetic field to further suppress nuclear spin field

9. Scalability • Initialization to Pure State • Qubit Read-out • Long Coherence Time • Universal Quantum Gates Far future--scaling Major Obstacles: • There is no well-defined protocol in tuning dots (e.g. Tuning is mainly based on trial an error even intuition sometimes; Lithographically identical structures behave differently due to impurities, which make ab initio simulation only meaningful in the studies of QDs qualitatively rather than quantitatively.) • Too many equipments are now needed to maneuver a single dot (even for the state of the art lab nowadays, to go beyond 10 qubits remains challenging ) • Long-distance communication for spin qubits

10. Summary • Electron spin manipulation by means of electrical field only is now proved to be feasible and of merits • Potential ways to improving manipulation techniques and coherence properties are given

11. Synchronized Double Pulses to Explore Two Spin at Once • The essence of this part is to extend single-shot read-out scheme of a single electron spin in a single-dot to two electron spins in a double-dot • Outline of this part : • First comes a brief review on the single-shot read-out experiment of one electron spin • Then we introduce the device configuration and method employed • Follows is the experimental details including setups, pre-adjustments, such as tuning and some notes about this experiments • Lastly is some analysis provided by the author and some personal ideas.

12. Brief Review • Pulses are applied to the gate P • The Quantum Point Contact (QPC) is very sensitive to the electrical field in the adjacent quantum dot, thus serves as a sensor to detect the electron bouncing into/out from the quantum dot • Basically, QPC current will mimic the shape of the pulse applied • However an electron bouncing into/out from the dot will result in a step in QPC current • Zeeman splitting induced energy difference makes spin-down electrons easy to escape

13. Brief Review Read-out pulse scheme Illustration of read-out strategy

14. Brief Review Key Question: ”How to tune the dot to the suitable read-out position?”

15. Device and Method Red: QPC related gates QL/QR: side gate SL/SR: used to isolate QPC’s source/drain from double-dot’s Black: Gates that define the double-dot Orange: Gates used for fine tuning of left/right dot respectively

16. Device and Method • As a routine, we obtain the stability diagram • Ensure that we can deplete the dots • From such gram we obtain “slopes” respectively as illustrated • According to the slope we can calculate the compensate parameter, Gamma. • After transformation, edges in such diagram becomes vertical/horizontal

17. Device and Method Take for instance Strategy I: read left and right dot in a set sequence Note: “both out”, “both in” in the first two stage was a simplification, without loss of generality, in fact, two electron do not necessarily go in or out at the same time.

18. Device and Method Strategy II: read left and right dot at once in a stochastic sequence Note:in the read-out stage, which kind shape of “bump” comes first is also stochastic. Lower bump indicate event happened in the non-adjacent, in this case, the right dot.

19. Device and Method Question: How to determine the relative height for different stage of the pulse? Relative height of the pulse can be determined by the honeycomb diagram

20. Key Question: How to determine the tune each dot to the read-out position? Blue: position of two spin state in “empty stage” Orange: that in “inject stage” Purple: that in “read-out stage”

21. Detail of Experiment • After the such step above is done, the optimum value to set VL to the read-out position has been determined • Then set the voltage applied to VL the optimum value, do the same thing for gate VR. Thus the pre-adjustment of read-out process has been finished Crucial Parameters • No bias is applied to source & drain; • Bias applied to the QPCs are 700V, under this circumstance, the current in through QPC is about 20nA; • Electron tunneling on/off in adjacent quantum dot will result in a bump in QPC current of the height about 200pA, such event happened in non-adjacent quantum dot corresponds to a bump 100pA, smaller by a factor of 2; • Tunnel rate to the left and right reservoir is about 1/(0.05ms); • If electron tunneling on and off last more than 8s as a whole, it can be detected. • A in-plain magnetic field of 5T is applied.

22. Analysis Comparison between two strategy: • Strategy II has a potential to do faster measurements. • Its fidelity lies in the capability to detect interdot tunneling, as when read-out the two spin at once, two energy level are aligned, exchange interaction will possibly mess up the two states • Strategy I is rather plain and normally has a higher fidelity, as when read-out two electron sequentially, the detuning will suppress the tunneling or exchange effect.

23. Analysis Can be tuned slightly different to prevent alignment thus exchange or tunneling during read-out

24. Analysis Difficulties: • Too few spin-downs are injected during a test of spin relaxation time (lowering B field) • Dilution refrigerator can not be cooled down to base temperature • In this case, a noise band • Synchronization of two pulses and About Labview in Windows OS. • From Hanson’s thesis, the spin-dependent tunneling rate.