Rapid high-temperature initialisation and readout of spins in silicon with 10 THz photons

Abstract

Each cycle of a quantum computation requires a quantum state initialisation. For semiconductor-based quantum platforms, initialisation is typically performed via slow microwave processes and usually requires cooling to temperatures where only the lowest quantum level is occupied. In silicon, boron atoms are the most common impurities. They bind holes in orbitals including an effective spin-3/2 ground state as well as excited states analogous to the Rydberg series for hydrogen. Here we show that initialisation temperature demands may be relaxed and speeds increased over a thousand-fold by importing, from atomic physics, the procedure of optical pumping via excited orbital states to preferentially occupy a target ground state spin. Spin relaxation within the orbital ground state of unstrained silicon is too fast to measure for conventional pulsed microwave technology, except at temperatures below 2 K, implying a need not only for fast state preparation but also fast state readout. Circularly polarised ~10 THz photon pulses from a free electron laser meet both needs at temperatures above 3 K: a 9 ps pulse enhances the population of one spin eigenstate for the "1s"-like ground state orbital, and the second interrogates this imbalance in spin population. Using parameters given by our data, we calculate that it should be possible to initialise 99% of spins for boron in strained silicon within 250 ps at 3 K. The speedup of both state preparation and measurement gained for THz rather than microwave photons should be explored for the many other solid state quantum systems hosting THz excitations potentially useful as intermediate states.

Figures (5)

• Figure 1: Excitation--relaxation cycle and experimental schematic.a-d Each step in an initialisation cycle, described in the main text. b shows the allowed transitions from the $1\Gamma_8^+$ ground state quartet to the $1\Gamma_{6,7}^{-}$ excited doublets for $\epsilon_{+}$ light propagating along $\langle111\rangle$. The faint red line indicates a near-zero transition rate Bhattacharjee1972. The laser spectrum overlaps differently with the excited states. e A beam-splitter (BS) splits the linearly-polarised FELIX pulse into pump and probe beams. The pump passes a translation stage to control the relative arrival time between the two pulses. Both beams then pass wire-grid polarisers that can be independently rotated to control the final polarisations incident on the silicon prism quarter wave plates (QWP). Both beams coincide on the 2.9K boron-doped silicon. The angle of incidence differs by $\sim$5° to filter the pump light out of the detector channel.
• Figure 2: Pump-probe raw data and circular dichroism during one initialisation cycle.a The time-resolved data depicting the change in transmission of the probe $\Delta \tau$ relative to the transmission of a constant reference probe $\tau$. The data come in pairs that overlap almost entirely. The labels 1a-1d mark the different parts of the initialisation process in Fig. \ref{['fig:cycle_schematic']}. At 1a all degenerate ground states are in thermal equilibrium and equally populated, representing the transmission baseline. At 1b a pump excites a subset of ground states, causing their populations to drop in 9ps. At 1c the excited states then quickly decay over the course of $\sim$36ps. At 1d the circularly polarised pumps have created an imbalance in the ground state populations and therefore a dichroism in the probe -- separating red and blue. A linear pump induced no dichroism (purple). Spin-lattice relaxation drives the slow decay back to equilibrium. The sample temperature was 2.9K and the pump pulse energy was $\sim$2.9nJ. The model described in the Quantum Dynamics section was fit simultaneously to all the data, and is shown for the SCP, OCP and PCP in the dark solid lines. Below is the circular dichroism, defined as the difference between the SCP (blue) and OCP (red) curves and plotted on a logarithmic scale. b The 'bright' ground states excited by the pump and then interrogated by the probe, for all polarisation combinations. An upwards arrow corresponds to that ground state spin population increasing as the excited holes decay after the pump's action.
• Figure 3: Temperature dependence of spin and orbital lifetimes.a OCP data for various temperatures between 2.9K and 11K. b Fast (orbital) and slow (spin) lifetimes as a function of temperature, extracted from the OCP data in a. Error bars represent the standard deviations, and are mostly smaller than the symbols. c Spin lifetimes from b are compared to those from previous microwave experiments ($T_{1}$, extracted either from time-resolved spin-echo measurements or from CW EPR linewidths, see Methods): Ludwig 1962 (stress: 490$\pm$30MPa) LUDWIG1962223, Dirksen 1989 (stress: 750MPa) Dirksen1989, Stegner 2010 Stegner2010, Tezuka 2010 Tezuka2010, Song 2011 Song2011 and Kobayashi 2021 (both unstressed and 30MPa stress) Kobayashi2021. Our experimental data are represented by circles. Literature results for unstrained silicon are shown as squares and for strained silicon as diamonds. Here we have applied a small correction to the measured temperatures for our data points (denoted by circles). The correction grows at lower temperatures as the sample temperature (exposed to background radiation through the cryostat windows) saturates while the (unexposed) thermometer temperature continues to drop. Details are in Supplementary Note 4.
• Figure 4: Optical pumping through different states.Top: SCP data (logarithmic y-axis) for transitions into the $1\Gamma_{6}^{-} + 1\Gamma_{7}^{-}$ states (blue) and into the $1\Gamma_{8}^{-}$ excited state (red). The fast initial decay was dependent on the excited state, but the final slow decay was not and closely matched to within each other's standard deviation. The pump energy for $1\Gamma_{6}^{-} + 1\Gamma_{7}^{-}$ was 1.6nJ, for $1\Gamma_{8}^{-}$ it was 5.9nJ, reflecting the difference in oscillator strengths Pajot2010. Bottom: OCP data for $2\Gamma_{8}^{-}$ compared to normalised OCP data for $1\Gamma_{6}^{-} + 1\Gamma_{7}^{-}$. The long lifetime components also match.
• Figure 5: Fits and simulations of target population.Bottom: The blue solid lines represent the quantum dynamics model result for the population of the target state $m_{J}=1/2$ for three different pump pulse energies: 9.0nJ, 2.9nJ and 0.9nJ, over the course of 1ns from the moment the pump arrives. The dichroism data for each energy are plotted alongside the modelled populations in red. We observed little power dependence of the spin relaxation time $T_{1}$ measured by our fits: the 9.0nJ, 2.9nJ and 0.9nJ pumps displayed $T_{1}=1020\pm19$, $1136\pm15$ and $1129\pm15$ picoseconds respectively. Top: The dashed lines are simulations of the target state population throughout a hypothetical 1ns laser pulse. The simulation in purple used the same parameters extracted from the 2.9nJ pump, apart from the pulse duration. In orange the spin lifetime was replaced with the value from a very similar boron-doped silicon sample at 45mK Song2011. In red is our simulation for an optimised scheme using strain and the $2\Gamma_{8}^{-}$ state as the intermediate state for optical pumping (see Supplementary Note 3).