Heiss W.D. (ed.) Quantum dots.. a doorway to - tiera.ru

More documents

Recommendations

Info

72 J.M. Elzerman et al. 5 Single-Shot Read-Out of an Individual Electron Spin in a Quantum Dot Spin is a fundamental property of all elementary particles. Classically it can be viewed as a tiny magnetic moment, but a measurement of an electron spin along the direction of an external magnetic field can have only two outcomes: parallel or anti-parallel to the field [65]. This discreteness reflects the quantum mechanical nature of spin. Ensembles of many spins have found diverse applications ranging from magnetic resonance imaging [66] to magneto-electronic devices [67], while individual spins are considered as carriers for quantum information. Read-out of single spin states has been achieved using optical techniques [68], and is within reach of magnetic resonance force microscopy [69]. However, electrical read-out of single spins [2, 49, 70, 71, 72, 73, 74, 75] hasso far remained elusive. Here, we demonstrate electrical single-shot measurement of the state of an individual electron spin in a semiconductor quantum dot [40]. We use spin-to-charge conversion of a single electron confined in the dot, and detect the single-electron charge using a quantum point contact; the spin measurement visibility is ∼65%. Furthermore, we observe very long singlespin energy relaxation times (up to ∼0.85 ms at a magnetic field of 8 Tesla), which are encouraging for the use of electron spins as carriers of quantum information. 5.1 Measuring Electron Spin in Quantum Dots In quantum dot devices, single electron charges are easily measured. Spin states in quantum dots, however, have only been studied by measuring the average signal from a large ensemble of electron spins [54, 68, 77, 78, 79, 80]. In contrast, the experiment presented here aims at a single-shot measurement of the spin orientation (parallel or antiparallel to the field, denoted as spin-↑ and spin-↓, respectively) of a particular electron; only one copy of the electron is available, so no averaging is possible. The spin measurement relies on spinto-charge conversion [54, 79] followed by charge measurement in a single-shot mode [58, 59]. Figure 28a schematically shows a single electron spin confined in a quantum dot (circle). A magnetic field is applied to split the spin-↑ and spin-↓ states by the Zeeman energy. The dot potential is then tuned such that if the electron has spin-↓ it will leave, whereas it will stay on the dot if it has spin-↑. The spin state has now been correlated with the charge state, and measurement of the charge on the dot will reveal the original spin state. 5.2 Implementation This concept is implemented using a structure [55] (Fig. 28b) consisting of a quantum dot in close proximity to a quantum point contact (QPC). The quantum dot is used as a box to trap a single electron, and the QPC is
a reservoir dot Semiconductor Few-Electron Quantum Dots as Spin Qubits 73 0 -e 0 -e Q dot Q dot Time Time b RESERVOIR Γ 200 nm T MP R I QPC DRAIN Q SOURCE Fig. 28. Spin-to-charge conversion in a quantum dot coupled to a quantum point contact. (a) Principle of spin-to-charge conversion. The charge on the quantum dot, Qdot, remains constant if the electron spin is ↑, whereas a spin-↓ electron can escape, thereby changing Qdot. (b) Scanning electron micrograph of the metallic gates on the surface of a GaAs/Al0.27Ga0.73As heterostructure containing a two-dimensional electron gas (2DEG) 90 nm below the surface. The electron density is 2.9 × 10 15 m −2 . (Only the gates used in the present experiment are shown, the complete device is describedin[55].) Electrical contact is made to the QPC source and drain and to the reservoir via Ohmic contacts. By measuring the current through the QPC channel, IQP C, we can detect changes in Qdot that result from electrons tunnelling between the dot and the reservoir (with a tunnel rate Γ ). With a source-drain bias voltage of 1 mV, IQP C is about 30 nA, and an individual electron tunnelling on or off the dot changes IQP C by ∼0.3 nA. The QPC-current is sent to a room temperature current-to-voltage convertor, followed by a gain 1 isolation amplifier, an AC-coupled 40 kHz SRS650 low-pass filter, and is digitized at a rate of 2.2×10 6 samples/s. With this arrangement, the step in IQP C resulting from an electron tunnelling is clearly larger than the rms noise level, provided it lasts at least 8 µs. A magnetic field, B, is applied in the plane of the 2DEG operated as a charge detector in order to determine whether the dot contains an electron or not. The quantum dot is formed in the two-dimensional electron gas (2DEG) of a GaAs/AlGaAs heterostructure by applying negative voltages to the metal surface gates M, R, andT . This depletes the 2DEG below the gates and creates a potential minimum in the centre, that is, the dot (indicated by a dotted white circle). We tune the gate voltages such that the dot contains either zero or one electron (which we can control by the voltage applied to gate P ). Furthermore, we make the tunnel barrier between gates R and T sufficiently opaque that the dot is completely isolated from the drain contact on the right. The barrier to the reservoir on the left is set [81] to a tunnel rate Γ ≈ (0.05 ms) −1 . When an electron tunnels on or off the dot, it changes the electrostatic potential in its vicinity, including the region of the nearby QPC (defined by R and Q). The QPC is set in the tunnelling regime, so that the current, IQP C, is very sensitive to electrostatic changes [44]. Recording B
Page 1 and 2:
Lecture Notes in Physics Editorial
Page 3 and 4:
W. Dieter Heiss (Ed.) Quantum Dots:
Page 5:
Preface Nanoscale physics, nowadays
Page 9 and 10:
Contents A Guide for the Reader ...
Page 11 and 12:
A Guide for the Reader Quantum dots
Page 13 and 14:
The Renormalization Group Approach
Page 15 and 16:
RG for Interacting Fermions 5 where
Page 17 and 18:
where � is a shorthand: � ≡ 3
Page 19 and 20:
RG for Interacting Fermions 9 These
Page 21 and 22:
RG for Interacting Fermions 11 is i
Page 23 and 24:
RG for Interacting Fermions 13 the
Page 25 and 26:
RG for Interacting Fermions 15 this
Page 27 and 28:
RG for Interacting Fermions 17 equa
Page 29 and 30:
� p � dθp = g 2π RG for Inter
Page 31 and 32: RG for Interacting Fermions 21 the
Page 33 and 34: References RG for Interacting Fermi
Page 35 and 36: Semiconductor Few-Electron Quantum
Page 39 and 40: 1.2 Implementations Semiconductor F
Page 43 and 44: GaAs n-AlGaAs AlGaAs GaAs Semicondu
Page 49 and 50: ε1 ε0 e Semiconductor Few-Electro
Page 53 and 54: 250 Ω twisted pair 20 MΩ powder
Page 61 and 62: 10 5 0 -5 Semiconductor Few-Electro
Page 63 and 64: G ( e / h) 2 2 1 0 Semiconductor Fe
Page 67 and 68: V R (V) V R (V) Semiconductor Few-E
Page 69 and 70: V L (V) -1.084 -1.082 -1.080 -1.078
Page 71 and 72: B // Semiconductor Few-Electron Qua
Page 77 and 78: a RESERVOIR 200 nm Semiconductor Fe
Page 81: 4.5 QPC Versus SET Semiconductor Fe
Page 85 and 86: a b c V P (mV) 10 5 0 ∆I QPC E F
Page 91 and 92: Spin-down counts 200 100 a Semicond
Page 101 and 102: 6.7 Unresolved Issues Semiconductor
Page 107 and 108: 98 M. Pustilnik and L.I. Glazman Co
Page 109 and 110: 100 M. Pustilnik and L.I. Glazman F
Page 111 and 112: 102 M. Pustilnik and L.I. Glazman (
Page 113 and 114: 104 M. Pustilnik and L.I. Glazman A
Page 115 and 116: 106 M. Pustilnik and L.I. Glazman t
Page 119 and 120: 110 M. Pustilnik and L.I. Glazman
Page 121 and 122: 112 M. Pustilnik and L.I. Glazman f
Page 123 and 124: 114 M. Pustilnik and L.I. Glazman 5
Page 125 and 126: 116 M. Pustilnik and L.I. Glazman U
Page 127 and 128: 118 M. Pustilnik and L.I. Glazman 5
Page 131 and 132: 122 M. Pustilnik and L.I. Glazman d
Page 133 and 134:
124 M. Pustilnik and L.I. Glazman G
Page 135 and 136:
126 M. Pustilnik and L.I. Glazman d
Page 137 and 138:
128 M. Pustilnik and L.I. Glazman 1
Page 139 and 140:
130 M. Pustilnik and L.I. Glazman 7
Page 141 and 142:
132 C.W.J. Beenakker e e N I N S Fi
Page 143 and 144:
134 C.W.J. Beenakker 2 Andreev Refl
Page 145 and 146:
136 C.W.J. Beenakker F E x 8d/hv ga
Page 147 and 148:
138 C.W.J. Beenakker and we have de
Page 149 and 150:
140 C.W.J. Beenakker A stroboscopic
Page 151 and 152:
142 C.W.J. Beenakker largely indepe
Page 153 and 154:
144 C.W.J. Beenakker The effective
Page 155 and 156:
146 C.W.J. Beenakker Fig. 6. Ensemb
Page 157 and 158:
148 C.W.J. Beenakker 1.4 1.2 1.0 0.
Page 159 and 160:
150 C.W.J. Beenakker 〈ρ(E)〉 =
Page 161 and 162:
152 C.W.J. Beenakker P 0.5 0.4 0.3
Page 163 and 164:
154 C.W.J. Beenakker P(x) 0.4 0.3 0
Page 165 and 166:
156 C.W.J. Beenakker tunnel/ Egap 4
Page 167 and 168:
158 C.W.J. Beenakker its momentum).
Page 169 and 170:
160 C.W.J. Beenakker E00 = π� =
Page 171 and 172:
162 C.W.J. Beenakker 〈ρ(E)〉 δ
Page 173 and 174:
164 C.W.J. Beenakker As described i
Page 175 and 176:
166 C.W.J. Beenakker 0.30 � Egap
Page 177 and 178:
168 C.W.J. Beenakker The τE-depend
Page 179 and 180:
170 C.W.J. Beenakker that a fully m
Page 181 and 182:
172 C.W.J. Beenakker (τ−,τ+), w
Page 183:
174 C.W.J. Beenakker 61. P. G. Silv
show all

Heiss W.D. (ed.) Quantum dots.. a doorway to - tiera.ru

Create successful ePaper yourself

Delete template?

Save as template?