Photoinduced charge-carrier dynamics in a semiconductor-based ion trap investigated via motion-sensitive qubit transitions

Ion trap systems built upon microfabricated chips have emerged as a promising platform for quantum computing to achieve reproducible and scalable structures. However, photoinduced charging of materials in such chips can generate undesired stray electric fields that disrupt the quantum state of the ion, limiting high-fidelity quantum control essential for practical quantum computing. While crude understanding of the phenomena has been gained heuristically over the past years, explanations for the microscopic mechanism of photogenerated charge carrier dynamics remains largely elusive. Here we present a photoinduced charging model for semiconductors, whose verification is enabled by a systematic interaction between trapped ions and photoinduced stray fields from exposed silicon surfaces in our chip. We use motion-sensitive qubit transitions to directly characterize the stray field and analyze its effect on the quantum dynamics of the trapped ion. In contrast to incoherent errors arising from the thermal motion of the ion, coherent errors are induced by the stray field, whose effect is significantly imprinted during the quantum control of the ion. These errors are investigated in depth, and methods to mitigate them are discussed. Finally, we extend the implications of our study to other photoinduced charging mechanisms prevalent in ion traps and discuss considerations in fabrication to reduce semiconductor charging.

Figure 1

Ion displacement by photoinduced electric field. (a) Simplified scheme of our chip trap structure near trap region with 935-nm laser. (b) An enlarged view of the trapping region with a schematic description of the photoinduced electric field. (c)–(f) Images of the ion displaced by the stray field from silicon substrate induced by scattered light as the power of the 935-nm laser was increased. (Color scale for each image was adjusted for better visibility.)

Figure 2

Band diagram representation of the semiconductor charging model. The semiconductor surface is at $x=0$, while the layer to the left of $x=0$ represents a native oxide layer. (a)–(c) Charging in the presence of fixed surface charges only (super-bandgap SPV). (a) The system in thermal equilibrium. The filled (empty) circles represent electrons (holes). (b) Carrier dynamics in (thermal) nonequilibrium. photogenerated electrons (blue, upper filled circles) are attracted to the surface and holes (red, lower empty circles) are repelled into the bulk. (c) The steady state of the system in nonequilibrium. A negative SPV is formed as a result of the charge distribution. (d)–(f) Charging in the presence of both fixed surface charges and interface states (SPV inversion). (d) The system in thermal equilibrium. The blue color bar represents the electron occupation probability of the interface state. (e) Carrier dynamics in (thermal) nonequilibrium. In addition to the charge distribution process explained in (b), electrons optically excited from the interface state can diffuse into the bulk and recombine with free holes via bulk defect states. (f) The steady state of the system in nonequilibrium. A positive SPV is developed as a result of the depletion of holes at the surface. $E_{\mathrm{C}}$ and $E_{\mathrm{V}}$ indicate the conduction and valence band edges, $E_{\mathrm{i}}$ and $E_{\mathrm{F}}$ the midbandgap and Fermi level, and $E_{\mathrm{b}}$ and $E_{\mathrm{fs}}$ the energy levels of the bulk defect state and the interface state

Figure 3

Numerical simulation results of the semiconductor charging model. (a)–(c) Spatial profiles of (a) $\delta \varphi$ (dark cyan), ${\varphi }_0$ (black dashed); (b) $\delta n$ (blue, left arrow), $\delta p$ (red, right arrow); (c) $n=n_0+\delta n$ (blue, left arrow), $p=p_0+\delta p$ (red, right arrow), and $n_0,p_0$ (black dashed), for various ${\mathrm{\Sigma }}_{\mathrm{fs}}$ with fixed photon flux $N_0=1\times {10}^{15} {\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$. Values of ${\mathrm{\Sigma }}_{\mathrm{fs}}$ are denoted in the legends in units of ${\text{10}}^{10} {\mathrm{cm}}^{-2}$. Inset in (a) shows values of $\delta \varphi$ at $x=0$ for different ${\mathrm{\Sigma }}_{\mathrm{fs}}$. From (b)–(c), it can be seen that the distinctive characteristic of a positive (negative) SPV is the widening (narrowing) of the surface depletion range in comparison to its range in thermal equilibrium. The orange vertical lines at $x=0.129$ µm correspond to the Debye-screening length (defined as $r_{+}$ in Appendix pp5-s1), which indicates that excess electrons in the bulk are mostly involved in screening. (d)–(e) Spatial profiles of (d) $\delta \varphi$ (dark cyan), ${\varphi }_0$ (black dashed); (e) $\overline{f_{\mathrm{s}}}$ (circle), ${\overline{f_{\mathrm{s}}}}_0\approx 1$ (dashed); and (f) $n$ (blue, left arrow), $p$ (red, right arrow), for various photon fluxes $N_0$ and fixed ${\mathrm{\Sigma }}_{\mathrm{fs}}=8\times {10}^{10} {\mathrm{cm}}^{-2}$. Inset in (d) shows values of $\delta \varphi$ at $x=0$ for different $N_0$. Saturation of SPV and surface depletion range appear as $\overline{f_{\mathrm{s}}}$ approaches 0. Dotted horizontal lines in (c) and (f) indicate $n_0={10}^5 {\mathrm{cm}}^{-3}$ (inset) and $p_0={10}^{15} {\mathrm{cm}}^{-3}$, for the case when surface charges and interface states are absent (flat initial bands). Throughout (a)–(f), ${\mathrm{\Sigma }}_{\mathrm{ss}}=1\times {10}^{11} {\mathrm{cm}}^{-2}$, while the remaining parameter values were chosen and fixed to best illustrate the described effects.

Figure 4

Experimental configuration. (a) Schematic cross-sectional illustration of the microfabricated chip with parallel and perpendicularly incident laser beams. (b) Energy level diagram of ${}^{171}\mathrm{Yb}{}^{+}$ with Raman transition for qubit control by pulsed laser beams.

Figure 5

Measurement for laser power and wavelength dependence of the laser-induced field magnitude. (a) Raman transition probabilities vs inner dc voltage shift for a range of 1055-nm laser power. (b) Inner dc compensation voltage vs 1055-nm laser power. (c) Spectral response of laser-induced electric fields with respect to the compensation voltage (left) and the SPV (right). The shaded region indicates the unstable trapping condition of the ion. (d) Normalized optical cross section vs. photon energy. The solid circles are the values used to fit the experimental data in (c), with each color corresponding to the respective wavelength. The solid line corresponds to the fitted curve for the Hulthén potential in Eq. (3) while the dashed lines indicate the two limiting cases from the quantum defect model [42, 52]. The vertical error bars in (a)–(c) indicate the 95% confidence intervals of the fit and the horizontal error bars indicate $\pm 50\%$ of the photon flux values, which reflects their overall uncertainties.

Figure 6

Raman beam pre-turn-on measurement. (a) Operation sequence of pre-turn-on measurement for Raman beam 3. After state initialization, the global beam is first turned on, and then the individual beam is turned on after a time interval of $\mathrm{\Delta }T$. Raman transition is driven for 80 µs, followed by state detection. (b) Result of pre-turn-on measurement for Raman beam 3. Transition probability is plotted with varying $\mathrm{\Delta }T$ and the laser detuning $\delta$. (c) Result of pre-turn-on measurement for Raman beam 1. The orange dashed lines serve as guides for the maximum values at each time interval.

Figure 7

Rabi oscillation and Bloch sphere trajectory under the influence of coherent errors induced by semiconductor charging and incoherent errors due to thermal decoherence. (a) Simulated Rabi oscillations for thermal states with the average phonon number ${\overline{n}}_0=0$ (light gray, dashed), 10 (gray, dotted), and 20 (black, solid). The trajectory on the Bloch sphere and the purity of the qubit state for each case is depicted, with the color map representing the flow of time (blue to red or dark to light gray). Traces of the purity and their corresponding Rabi oscillations for identical ${\overline{n}}_0$ are represented using the same line styles. (b) Pre-turn-on applied, fully compensated ($t_{\mathrm{pre}}\gg {\tau }_{\mathrm{str}}, E_{\mathrm{com}}=E_{\mathrm{str}}$). The initial mean phonon number is fitted to ${\overline{n}}_0=6$. Comparing with the simulation for ${\overline{n}}_0=0$, the main source of damping occurs from motional decoherence. (c) Pre-turn-on applied, uncompensated ($t_{\mathrm{pre}}\gg {\tau }_{\mathrm{str}}, E_{\mathrm{com}}-E_{\mathrm{str}}=47\mathrm{V}{\mathrm{m}}^{-1}$). The initial mean phonon number is fitted to ${\overline{n}}_0=14$. (d) Pre-turn-on not applied, uncompensated ($t_{\mathrm{pre}}=0,{\tau }_{\mathrm{str}}=6$ µs, $E_{\mathrm{str}}=9\mathrm{V}{\mathrm{m}}^{-1}, E_{\mathrm{com}}=34\mathrm{V}{\mathrm{m}}^{-1}$). The initial mean phonon number is fitted to ${\overline{n}}_0=11$. (e) Pre-turn-on not applied, uncompensated ($t_{\mathrm{pre}}=0,{\tau }_{\mathrm{str}}=19$ µs, $E_{\mathrm{str}}=27\mathrm{V}{\mathrm{m}}^{-1}, E_{\mathrm{com}}=57\mathrm{V}{\mathrm{m}}^{-1}$). The initial mean phonon number is fitted to ${\overline{n}}_0=13$. (f) Sideband spectra depending on the application of the pre-turn-on sequence. The top (bottom) plot is obtained when pre-turn-on is utilized (not utilized). Throughout (b)–(e), the dark solid lines are fitted to data, while the gray dashed (solid) lines indicate simulation results corresponding ${\overline{n}}_0=0$ in (b)–(c) [(d)–(e)]. The purity is represented in solid (dashed) lines for the fitted (${\overline{n}}_0=0$) data. The experimental Rabi frequency and heating rate are $\mathrm{\Omega }=2\pi \times 78$ kHz and $\mathrm{\Gamma }\approx {10}^4$ quanta/s, respectively, for all cases. The simulated ion displacements are on the order of 10 nm – 100 nm, comparable to the wavelength of the driving laser.

Figure 8

Geometric interpretation of thermal decoherence on the Bloch sphere. An initial state $|i\rangle$ that undergoes thermally damped Rabi oscillation around a rotational axis on the equator of the Bloch sphere will spiral in towards the center of the circle $\mathcal{C}$ with radius $r_c$ (the rotational axis, quantum state, and radius $r_c$ are colored in purple, orange, and red, respectively). This is because components of the state with different Rabi frequencies originating from the phonon distribution will spread, adding up incoherently during the evolution. This process is schematically depicted in the left figure, where carrier Rabi frequencies for the oscillator states $|n\rangle$ and $|m\rangle$ are denoted as ${\mathrm{\Omega }}_{n,n}$ and ${\mathrm{\Omega }}_{m,m}$, respectively. The vector in orange represents the quantum state losing purity within a time interval $\mathrm{\Delta }t$. The extent of the spread is proportional to the radius $r_c=\cos \theta$, thus, resulting in a greater loss of purity as $r_c$ increases. In the right figure, the vector in orange represents the qubit state with the lowest purity given by ${\gamma }_{\mathrm{pur},\min }=0.5+\sin \theta$, assuming $|i\rangle$ and the specified rotational axis.

Figure 9

Band diagram of a semiconductor in thermal equilibrium. Note that the energy level is defined as $E=-\beta \varphi$ for the corresponding potentials $\varphi$. $E_{\mathrm{C}}$ and $E_{\mathrm{V}}$ indicate the conduction and valence band edges, respectively.

Figure 10

Plot of ${\tau }_{+}$ and ${\tau }_{-}$ for varying $n_{\mathrm{i}}$. The horizontal dashed line is set by ${\tau }_{\mathrm{eff}}=$ 1 s, while the vertical dashed line indicates the near-degenerate point of ${\tau }_{+}$ and ${\tau }_{-}$.

Figure 11

SEM image and COMSOL geometry for numerical simulations. (a) An SEM image of the cross section of the ion trap near the trapping region. (b) COMSOL simulation geometry corresponding to (a) with equipotential lines plotted when a voltage of $+1$ V is formed on the inclined surface of the silicon substrate (in red). Yellow arrows represent incident light and $l$ the semiconductor slab thickness.