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Few-Electron Quantum Dots for Quantum Computing

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Few-Electron Quantum Dots for Quantum Computing Few-electron quantum dots for quantum computing I.H. Chana, P. Fallahib, A. Vidanb, R.M. Westervelta,b, M. Hansonc, and A.C. Gossardc. a Department of Physics, Harvard University, Cambridge, MA 02138, USA b Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA c Materials Department, University of California at Santa Barbara, CA 93106, USA Classification numbers: 73.23.Hk Electronic transport in mesoscopic systems (Coulomb blockade, single-electron tunneling); 73.63.Kv Electronic transport in nanoscale materials and structures (quantum dots); 73.21.La Electronic states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems (quantum dots) Two tunnel-coupled few-electron quantum dots were fabricated in a GaAs/AlGaAs quantum well. The absolute number of electrons in each dot could be determined from finite bias Coulomb blockade measurements and gate voltage scans of the dots, and allows the number of electrons to be controlled down to zero. The Zeeman energy of several electronic states in one of the dots was measured with an in-plane magnetic field, and the g-factor of the states was found to be no different than that of electrons in bulk GaAs. Tunnel-coupling between dots is demonstrated, and the tunneling strength was estimated from the peak splitting of the Coulomb blockade peaks of the double dot. superconducting rings (Mooij et al., 1999). 1. Introduction These proposals are challenging experimentally. Recent progress in semiconductor quantum dots Interest in quantum computation has soared includes measurements of individual few- since the discovery that quantum computers electron quantum dots (Ashoori, 1996; Tarucha perform certain calculations exponentially faster et al., 1996; Gould et al., 1999) and double few- than a classical computer (Shor, 1997; Grover, electron quantum dots (Elzerman et al., 2003). 1997). Demonstrations that quantum In addition, the Zeeman energy was measured computation is experimentally feasible using for electrons in small quantum dots (Hanson et nuclear magnetic resonance techniques provided al., 2003; Potok et al., 2003). experimental motivation (Chuang et al., 1998; In this paper, we discuss measurements on Vandersypen et al., 2001), but a more scalable tunnel-coupled few-electron quantum dots, system is desired for quantum computation. which serve as the building blocks for a Numerous proposals for the physical realization quantum computer, as proposed by Loss and of a quantum computer provide several DiVincenzo (1998). The quantum bit (qubit) of promising avenues of research in the information would be encoded in the spin of an implementation of quantum computers. These individual electron that is physically contained include using the spins of electrons confined in inside a small semiconductor quantum dot. quantum dots (Loss and DiVincenzo, 1998), the Quantum computation would then be performed nuclear spins of phosphorus atoms embedded in on an array of quantum dots by sequences of crystalline silicon (Kane, 1998), the electronic spin-flip and “square-root of swap” (swap1/2) states of ions in optical traps (Cirac and Zoller, operations on the spins. These operations, which 1999), and persistent currents in can be classified into single-qubit (spin-flip) and 1 two-qubit (swap1/2) operations, were shown to The lithographic size of the dot is nominally be the minimal set needed to construct a 250´260 nm2. universal quantum computer (DiVincenzo, The few-electron dots were designed such 1995). The spin-flip operation would be carried that the tunnel-barriers to the leads were spaced out using electron-spin resonance (ESR) to flip as closely as possible, following the work of the spin of individual electrons, while the Gould et al. (1999). This was done to maximize swap1/2 operation would entangle a pair of spins the probability that both leads are connected to by controlling the tunneling between the the same puddle of electrons inside the dot, as quantum dots. Spin-selective filters (Folk et al., the electrostatic potential in small quantum dots 2003) may then be used to read out the results of is not perfectly smooth. The mental picture that the calculation. One key experimental hurdle helps explain why this is so is that of a pond. that must be overcome is storing just one When a pond (dot) is filled with water electron in each quantum dot. We present data (electrons), the pond is a contiguous mass of that demonstrates the possibility of storing a water. However, when the pond is drained and single electron in each of the two few-electron close to being empty, isolated puddles of water dots. The g-factor of electron spins was start to form within the pond due to the measured and found to be no different from that unevenness of the bottom of the pond in bulk GaAs, and tunnel-coupling between two (roughness of the potential inside the quantum few-electron dots was demonstrated. dot). Having electrical leads close to the same part of a dot therefore increases the chance that 2. Experimental Setup both are connected to the same puddle of electrons. The scanning electron micrograph in The few-electron dot device was measured in Figure 1(a) shows a few-electron double dot an Oxford Instruments Kelvinox 100 dilution device used in these experiments. The light gray refrigerator with a base temperature T = 70 mK areas are tunable Cr:Au gates fabricated using (kBT = 6 µeV). The measurement setup is shown electron-beam lithography on a GaAs/AlGaAs in Figure 1(b). The two few-electron dots were heterostructure containing a two-dimensional in series, so one lock-in amplifier and current electron gas (2DEG) located 52 nm beneath the preamplifier could be used to measure the surface. The wafer was grown by molecular conductance of either dot or both dots. Gate beam epitaxy, and consists of the following voltages were computer controlled. A layers (from the surface down): 50 Å GaAs, superconducting magnet inside the Kelvinox 250 Å Al0.3Ga0.7As, Si d-doping, 220 Å 100 Dewar provided an in-plane magnetic field Al0.3Ga0.7As, 200 Å GaAs, 1000 Å Al0.3Ga0.7As, up to 7 T. a 20-period GaAs/ Al0.3Ga0.7As superlattice, a 3000 Å GaAs buffer, and finally the semi- 3. Transport Measurements insulating GaAs substrate. This configuration places the 2DEG in a square-well potential. The We perform a series of experiments to 2DEG was measured to have a mobility demonstrate that each quantum dot in our few- µ = 470,000 cm2/Vs and a density electron double dot device can contain either N = 3.8´1011 cm-2 at 4 K. A square-well was zero, one or two electrons, as required by the used to get better confinement of the electrons Loss- DiVincenzo proposal for a semiconductor in the z-dimension. This allows greater control quantum computer. In our experiments, we first of the few-electron quantum dots because we completely emptied the dots of all electrons and are able to electrostatically push the electrons then used the Coulomb blockade effect to out of the dot using the surface metal gates effectively fill the dots back up, one electron at without leaking electrons out in the z-direction. a time, to the desired number. 2 3.1 Single-Dot Finite Bias Coulomb Blockade 3.2 Three-Dimensional Scan of a Few- Measurements Electron Dot The number of electrons on each quantum A drawback of using the finite bias Coulomb dot can be determined from finite bias Coulomb blockade technique for laterally-defined dots is blockade measurements. When the Coulomb that stray capacitance couples the sidegate blockade diamond is observed not to close, it voltage to the tunnel barriers of the dot and indicates that there are no more electrons left in causes them to get progressively more opaque. the dot. By energizing only the gates needed to This problem of a diminishing conductance form either dot, the finite bias Coulomb signal can be overcome by re-tuning the blockade for each dot may be measured quantum point contact (QPC) voltages, thereby separately, as shown in Figure 2. Figure 2(a) controlling the tunnel barrier heights, every time shows the differential conductance dGD1/dVDS the sidegate voltage is changed. The resulting of Dot 1 as a function of its sidegate voltage VG1 three-dimensional scan in the sidegate and QPC and the dc source-drain bias VDS, where GD1 is voltages, which are all the gate voltages that the conductance of Dot 1. Figure 2(b) shows the may be adjusted, also shows that the Coulomb corresponding differential conductance blockade peaks end and therefore that our dots dGD2/dVDS of Dot 2 as a function of its sidegate can be emptied of electrons. voltage VG2 and the dc source-drain bias VDS, Figure 3 shows the three-dimensional where GD2 is the conductance of Dot 2. The conductance data of Dot 2 as a series of two- Coulomb blockade diamonds for both dots are dimensional scans in QPC gate voltages VQPC1 visible as black diamonds, and the additional and VQPC2 as sidegate voltage VG2 goes from (a) lines parallel to the sides of the diamonds are –0.500 V to (f) –1.625 V in steps of –0.225 V. Coulomb blockade peaks from excited states of Each two-dimensional scan is a re-tuning of the the dots. As the sidegate voltages of both dots QPC gate voltages to Dot 2, and maximizes the are made more negative, the last Coulomb Coulomb blockade peak height of the Coulomb blockade diamond for each dot did not close. No blockade peaks within the scan. evidence of other Coulomb blockade peaks was As sidegate voltage VG2 is made more seen at drain-source biases out to 9 mV for Dot negative in Figures 3 (a) to (f), the Coulomb 1 and 7 mV for Dot 2.
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