Single-Shot Readout of Electron Spin States in a Quantum Dot Using Spin-Dependent Tunnel Rates

Abstract

We present a method for reading out the spin state of electrons in a quantum dot that is robust against charge noise and can be used even when the electron temperature exceeds the energy splitting between the states. The spin states are first correlated to different charge states using a spin dependence of the tunnel rates. A subsequent fast measurement of the charge on the dot then reveals the original spin state. We experimentally demonstrate the method by performing read-out of the two-electron spin states, achieving a single-shot visibility of more than 80%. We find very long triplet-to-singlet relaxation times (up to several milliseconds), with a strong dependence on in-plane magnetic field.PACS numbers: 03.67. Lx,73.63.Kv, The spin of electrons in semiconductors is the subject of extensive research, partly motivated by the prospects of using the spin as a classical bit [1] or a quantum bit [2]. Electron spins can be conveniently studied when confined to a semiconductor quantum dot, since here the number of electrons can be precisely controlled (down to zero) [3,4], the tunnel coupling to the reservoir is tunable over a wide range [4] and single-electron tunneling can be monitored in real-time using a nearby quantum point contact (QPC) [5,6] or a single-electron transistor [7,8] as an electrometer. For applications in quantum computing as well as for fundamental research such as a measurement of Bell's inequalities, it is essential that the spin state of the electrons can be read out.The magnetic moment associated with the electron spin is tiny and therefore hard to measure directly. However, by correlating the spin states to different charge states and subsequently measuring the charge on the dot, the spin state can be determined [2]. Such a spin-tocharge conversion can be achieved by positioning the spin levels around the electrochemical potential of the reservoir µ res as depicted in Fig. 1a, such that one electron can tunnel off the dot from the spin excited state, |ES , whereas tunneling from the ground state, |GS , is energetically forbidden. By combining this scheme with a fast (40 kHz bandwidth) measurement of the charge dynamics, we have recently performed read-out of the spin orientation of a single electron, with a single-shot visibility up to 65% [9]. (A conceptionally similar scheme has also allowed single-shot read-out of a superconducting charge qubit [10]). However, this energy-selective readout (E-RO) has three drawbacks: (i) E-RO requires an energy splitting of the spin states larger than the thermal energy of the electrons in the reservoir. Thus, for a single spin the read-out is only effective at very low electron temperature and high magnetic fields (8 T and higher in Ref. [9]). Also, interesting effects occurring close to degeneracy, e.g. near the singlet-triplet crossing for two electrons [11], can not be probed. (ii) Since the E-RO relies on precise positioning of the spin levels with respect to the reservoir, it is very sensitive to fluctuations in the electrostatic potential. Backg...

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“…While we refer the reader to Refs. 39,40,41,42,43 for the details, we will give a simplified thumb-nail sketch of the physics here.…”

“…Therefore results (40,41,42) can be extended using this symmetry. Combining results, we can now calculate the total uncollapsing probability, P S =p 1 P C,1 +p 2 P C,2 to obtain the result (32) in this new, more powerful way.…”

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