1. Coherent interactions at a distance provide a powerful tool for quantum simulation and computation. The most common approach to realize an effective long-distance coupling ‘on-chip’ is to use a quantum mediator, as has been demonstrated for superconducting qubits and trapped ions. For quantum dot arrays, which combine a high degree of tunability with extremely long coherence times, the experimental demonstration of the time evolution of coherent spin–spin coupling via an intermediary system remains an important outstanding goal. Here, we use a linear triple-quantum-dot array to demonstrate a coherent time evolution of two interacting distant spins via a quantum mediator. The two outer dots are occupied with a single electron spin each, and the spins experience a superexchange interaction through the empty middle dot, which acts as mediator. Using single-shot spin readout, we measure the coherent time evolution of the spin states on the outer dots and observe a characteristic dependence of the exchange frequency as a function of the detuning between the middle and outer dots. This approach may provide a new route for scaling up spin qubit circuits using quantum dots, and aid in the simulation of materials and molecules with non-nearest-neighbour couplings such as MnO , high-temperature superconductors and DNA. The same superexchange concept can also be applied in cold atom experiments.
Leon Camenzind
FAM,

2. The exchange Gate (SWAP)
𝑡 𝑁 𝜖
𝐽 ~ 𝑡 𝑁 2 /𝜖
𝜙=𝐽 𝜖 𝜏 𝐸 /ℏ
Petta et al., Science 2005
𝜖→−∞, separate dot
𝜖=0
Martins et al., PRL116 (2015)

3. ≫ Exchange Interaction 𝑡 𝑁
𝐽 𝑁 ~ 𝑡 𝑁 2 𝜖 𝑡 𝑁 : nearest-neighbour tunnel coupling
𝜖: detuning of dots

4. Quantum Mediator→ Superexchange
«Virtual Transition»: virtual occupation of a non-magnetic intermediate state t
𝐽 𝑆𝐸 ~ 𝑡 𝑚,𝑙 2 𝑡 𝑚,𝑟 2 𝛿 2 𝜖 𝛿: detuning of intermediate quantum mediator.
𝜖: detuning of outer dots
𝐽 𝑆𝐸
See e.g.: Erich Koch, Exchange Mechanisms, Lecture Notes
Kramers, H. L’interaction entre les atomes magnétogènes dans un cristal paramagnétique. Physica 1, 182–192 (1934) →𝑀 𝑛 2 𝑂

5. Motivation I – large range SWAP gate
SWAP Operation on a network of Qbits
Tunable
Quantum Mediator
qubit
All electrical
Turn on/off of J gate

6. Sources of for spin projection change:
charge exchange with the reservoirs (control ~ 10 −5 )
hyperfine interaction 𝛿 𝐵 ⊥ ~7𝑚𝑇 vs 3.5T → 10 −6 flips per transfer
spin–orbit (SO) interaction
Experiment: no spin rotation due to shuttling
Scarlino et al., PRL 113 (2014)

7. Long-range transfer using second order tunneling
Detuning of Middle Dot
See also

8. Back to Superexchange: Spin Relaxation and Measurement Scheme
Readout 1 vs time
B = 3.2T
Readout fidelities of 95.9% and 98.0% for spin species
Spins completely separated
L+R are «virtual gates»: compensating crosscapacitances
We have ~ 147ms for this configuration || 10ms for 3.2T

9. Measurement scheme In Detunig space F Mixture | ↑0↓ 𝑎𝑛𝑑 | ↑0↑
Spins well separated J=0

10. Superexchange-driven spin oscillations
𝐽 𝑁 ~ 𝑡 𝑁 2 𝜖
𝐽 𝑆𝐸 ~ 𝑡 𝑚,𝑙 2 𝑡 𝑚,𝑟 2 𝛿 2 𝜖
𝜙=𝐽 𝜖 𝜏 𝐸 /ℏ
From EDSR: Δ 𝐸 𝑍 ~130𝑀𝐻𝑧 𝑡 𝑚,𝑙 =8.5 𝐺𝐻𝑧= 𝑡 𝑁 𝑡 𝑚,𝑟 =11.8 𝐺ℎ𝑧

11. From Superexchange to nearest Neigbour exchange
𝐽 𝑁 ~ 𝑡 𝑁 2 𝜖 𝑙,𝑚 ~ 𝑡 𝑁 2 𝛿
𝐽 𝑆𝐸 ~ 𝑡 𝑚,𝑙 2 𝑡 𝑚,𝑟 2 𝛿 2 𝜖
𝛿>0
𝜙=𝐽 𝜖 𝜏 𝐸 /ℏ
𝛿<0
𝜖=−120𝜇𝑒𝑉
𝐽 𝑁
𝐽 𝑆𝐸
Δ 𝐸 𝑧
J up to 900 MHz

12. Conclusion
Quantum Dot array with very good control + subsequentual spin read out
Quantum gate between spins at distance via virtual occupation of a quantum mediator
Δ 𝐸 𝑧 → 𝐽 𝑆𝐸 → 𝐽 𝑁 and good agreement with theory

13. M=-42mV
M=-56mV

14. Simplified argument M=0 M=0 M ≠ 0
Erich Koch, Exchange Mechanisms, Lecture Notes

15. M=-412mV
M=-382mV
L+R are «virtual gates»: compensating crosscapacitances

18. TU Delft