Figure 1

(a) An SEM micrograph of the Cooper-pair box and SET electrometer. The device is made from an evaporated aluminum film (light gray regions) on an insulating $\mathrm{S}\mathrm{i}{\mathrm{O}}_{\mathrm{2}}$ substrate (dark gray regions) by the technique of double angle evaporation [8], which gives the double image. The aluminum has BCS gap $\Delta /k_B=2.4\mathrm{K}$. (b) A circuit diagram of the box and RF-SET electrometer. The SET gate voltage $V_{ge}$, the 500 MHz oscillatory bias, and the dc bias ($\mathrm{R}{\mathrm{F}}_{\mathrm{i}\mathrm{n}}\mathrm{+}\mathrm{d}\mathrm{c}$) determine the electrometer’s operating point. The charge on the box is inferred from variation in the amount of applied RF power that is reflected ($\mathrm{R}{\mathrm{F}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$) from the SET electrometer, which is a sensitive function of SET’s conductance [9]. The tunnel junctions (crosses in boxes) are characterized by a junction resistance $R_J$ and capacitance $C_J$, which enter the box’s Hamiltonian through $C_{\Sigma }=C_C+2C_J+C_g$ and $R_{\Sigma }=R_J/2$ (see text).Reuse & Permissions

Figure 2

(a) The ground and excited state energies versus $n_g$ for Eq. (1), with $4E_C=12E_J$ (solid line) and $E_J=0$ (dotted lines). Energy eigenstates asymptotically approach charge states ($|1⟩$ and $|0⟩$) far from $n_g=0.5$. (b) $Q_{\mathrm{b}\mathrm{o}\mathrm{x}}$ vs $n_g$, calculated for the ground state (dotted line), excited state (dashed line), and measured (solid line) with 35 GHz microwaves applied to the box gate. The arrows indicate resonant peaks. Also shown is $Q_{\mathrm{b}\mathrm{o}\mathrm{x}}$ measured with no microwaves applied (solid line), with the $y$ axis shifted down by $2.2e$. (c) Two resonant peaks in $Q_{\mathrm{b}\mathrm{o}\mathrm{x}}$ vs $n_g$ on the bottom axis and vs ${\omega }_{01}$ on the top axis, with $\omega =38\mathrm{G}\mathrm{H}\mathrm{z}$ and where the larger value of $V_g^{ac}$ (squares) is twice the smaller value (triangles).Reuse & Permissions

Figure 3

Resonant spectroscopy of the box versus the two control parameters of the Hamiltonian, $V_g$ and $\Phi$. (a) The locations of resonant peaks (circles) in $n_g$ and $\Phi$, for $\omega =32$, 35, and 38 GHz and fits (lines), using Eq. (1) for ${\omega }_{01}=2\omega =64$, 70, and 76 GHz to find a single value of $E_C$ and of $E_J^{\mathrm{m}\mathrm{a}\mathrm{x}}$. The systematic uncertainty in $n_g$ is represented by the size of the open circle symbols. (b) The height, in electrons, of a 76 GHz resonant peak as a function of $\Phi$ (squares) and a guide to the eye (line).Reuse & Permissions

Figure 4

A determination of the excited-state lifetime of the box. $Q_{\mathrm{b}\mathrm{o}\mathrm{x}}$ vs time $t$ (triangles), relative to $t=0$, when $n_g$ is shifted from $=0.248$ to 0.171 in 30 ns, with 38 GHz microwaves applied. The shift in $n_g$ brings the box out of resonance with the microwave excitation. An exponential fit to the data implies $T_1=1.3\mu \mathrm{s}$ (line).Reuse & Permissions