Optical switching of resonance fluorescence from a single germanium vacancy color center in diamond

TL;DR

This paper demonstrates a method to control and amplify resonance fluorescence from single germanium vacancy centers in diamond using a weak non-resonant laser, enabling stable quantum emitter operation for scalable quantum networks.

Contribution

It introduces a controlled gating technique to recover and enhance resonance fluorescence in GeV centers, improving their stability for quantum network applications.

Findings

Resonance fluorescence can be stabilized using weak non-resonant laser gating.

Gated excitation enhances fluorescence stability of GeV centers.

Method paves the way for reliable quantum emitters in diamond.

Abstract

Scalable quantum photonic networks require coherent excitation of quantum emitters. However, many solid-state systems can undergo a transition to a dark shelving state that inhibits the fluorescence. Here we demonstrate that a controlled gating using a weak non-resonant laser, the resonant excitation can be recovered and amplified for single germanium vacancies (GeVs). Employing the gated resonance excitation, we achieve optically stable resonance fluorescence of GeV centers. Our results are pivotal for the deployment of diamond color centers as reliable building blocks for scalable solid state quantum networks.

Equations

$$\displaystyle\frac{d}{dt}\left(\begin{array}[]{ccccc}\rho_{\text{G}},&\rho_{\text{E}},&\rho_{\text{GE}},&\rho_{\text{EG}},&\rho_{\text{D}}\end{array}\right)^{\text{T}}=$$

$$\displaystyle\left(\begin{array}[]{ccccc}-k_{\text{GD}}&\Gamma_{\text{sp}}&i\Omega/2&-i\Omega/2&k_{\text{DG}}\\ 0&-\Gamma_{\text{sp}}-k_{\text{ED}}&-i\Omega/2&i\Omega/2&0\\ i\Omega/2&-i\Omega/2&-1/T_{2}&0&0\\ -i\Omega/2&i\Omega/2&0&-1/T_{2}&0\\ k_{\text{GD}}&k_{\text{ED}}&0&0&-k_{\text{DG}}\end{array}\right)\left(\begin{array}[]{c}\rho_{\text{G}}\\ \rho_{\text{E}}\\ \rho_{\text{GE}}\\ \rho_{\text{EG}}\\ \rho_{\text{D}}\end{array}\right)$$

$$\Delta \nu =\frac{1}{\pi T_2}\sqrt{1+\frac{1}{2}\frac{{\Omega }^2{T}_2(k_{\text{ED}}+2k_{\text{DG}}+k_{\text{GD}})}{({\Gamma }_{\text{sp}}+k_{\text{ED}})(k_{\text{DG}}+k_{\text{GD}})}}$$

$$I_{\text{PL}}(t)=\eta {\Gamma }_{\text{sp}}{\rho }_{\text{E}}(t)$$

Full text

Artificial atomic systems that can be coherently controlled and manipulated are of a paramount importance for realization of scalable quantum photonic architectures Aharonovich and Neu (2014); Atatüre et al. (2018). Recently, color centers in diamond, particularly group IV defects, such as the silicon vacancies (SiV) Neu et al. (2011a) or the germanium vacancies (GeV) Iwasaki et al. (2015); Palyanov et al. (2015); Häußler et al. (2017); Bhaskar et al. (2017); Siampour et al. (2018); Bray et al. (2018) have emerged as attractive candidates. These defects possess an inversion symmetry Hepp et al. (2014) and therefore are not sensitive to local fluctuation in electric fields, resulting in a robust optical fluorescence with high indistinguishability Sipahigil et al. (2014). Additional advantage of those systems is their high Debye Waller factor that is manifested in a significant portion of the emission being concentrated in the zero phonon line (ZPL) Neu et al. (2011b); Palyanov et al. (2015). This high concentration makes their resonance fluorescence (RF) appealing for efficient long-distance quantum communication Duan et al. (2001), quantum teleportation Bouwmeester et al. (1997) and entanglement swapping Pan et al. (1998).

Unfortunately, under resonant excitation, these systems can undergo a non-radiative transition to a dark state, resulting a quenching of RF. For the nitrogen vacancy (NV) centers Doherty et al. (2013), this is often associated with a charge-state transition from negative to neutral Waldherr et al. (2011); Siyushev et al. (2013). Such a process results in lack of photons under resonant excitation, and consequently hinder the potential for single shot spin readout Sukachev et al. (2017); Vamivakas et al. (2010), and continuous operation of the quantum network Kimble (2008). Here we show that the quenching of RF also occurs for GeV color centers. In the positive side, we find that the RF can be reinstated by employing a small amount of non-resonant beam at 532 nm. This laser acts as a gate control over the fluorescence from the emitter, which can be quantitatively modeled by using a 2-level system accompanied by a dark-state.

The investigated sample consists of implantation-generated GeV centers within an electronic-grade Type IIa diamond GeV . The implanted Ge atom takes the interstitial space between the two empty carbon sites, forming a unique split-vacancy configuration with D3d symmetry, as shown in Fig. 1(a). Due to the strong spin-orbit coupling Thiering and Gali (2018), the ground state (${}^{2}\text{E}_{g}$) and excited state (${}^{2}\text{E}_{u}$) split into a pair of energy levels with two-fold spin-degeneracy at zero magnetic field, leading to the characteristic four-line fine structure in the ZPL emission spectrum at 602 nm [Fig. 1(b)]. To enhance the photon collection efficiency, a half-sphere solid immersion lens (SIL) with a diameter of 5 $\mu$m is fabricated on top of the sample by using focused ion (Ga+) beam (FIB) milling before Ge implantation Marseglia et al. (2011); GeV , as shown in Fig. 1(c). The sample is mounted on a XYZ piezo-stepper motorized stage housed in a closed-cycle helium-flow cryostat at 5 K.

All optical measurements are performed by using a home-built confocal microscope, as shown in Fig. 1(a). An achromatic microscopic objective with NA=0.9 is placed one focal length away from the sample to focus the excitation beam into the SIL and collect the PL from the emitter. A tunable continuous-wave (cw) laser with a linewidth of $<1$ MHz is used to resonantly address the GeV center, and perform photoluminescence excitation (PLE) measurements. A diode-pumped solid-state laser at 532 nm is used for non-resonant excitation of the emitter and gating of RF, enabled by passing through an acousto-optic modulator (AOM). After directed through a band-pass filter, the PL is coupled into a single-mode fiber connected to a spectrometer or a single-photon avalanche detector (SPAD). In PL spectrum characterization, a $600\pm 7$ nm band-pass filter is used for ZPL detection; in PLE and gating experiments, a $650\pm 20$ nm band-pass filter is used for phonon-side band (PSB) PL detection.

The gating effect by the non-resonant laser can be demonstrated by comparing PLE spectra with the gating laser on or off, as shown in Fig. 2(a). For both transitions C and D, the PLE spectra are only detectable when the gating laser is on. The multiple peaks around transition C possibly originate from the nearby GeV centers, whose associated D lines are shifted out of the measurement window thanks to the different strains experienced by centers GeV . The PL intensity is enhanced by 500 folds when switching on the gating laser, as shown in Fig. 2(b), where the gating power is $\sim$10*-4* of non-resonant saturation power P${}_{1}=6.8\pm 0.1$ mW GeV . In fact, this non-resonant beam is too weak to induce any detectable fluorescence from the emitter [right panel of Fig. 2(b)], and the main role played by this light is a switch controlling the on and off of the RF from the emitter. We stress that the optical pumping between the two ground states cannot account for the observation because the orbital relaxation, T${}_{1}^{\text{orbital}}\simeq 20$ ns Siyushev et al. (2017), is orders of magnitude faster than the gating dynamics involved here. Instead, a long-lived dark state is resorted for the explanation, evident by the bunching plateau of second-order correlation function and the stochastic jumping of RF, as shown in Fig. 2(c) Nguyen et al. (2013); Delteil et al. (2014). Even with the presence of dark state, coherence between ground and excited states can still be generated and maintained for a coherence time of T${}_{2}=366\pm 20$ ps, as shown by the Rabi oscillation of transition C in Fig. 2(d). Since both transitions C and D are equivalent for our study, we focus on the latter for the rest of the Letter for the sake of clarity.

To understand the photodynamics in the system, we study the power dependence of RF by varying either the resonant [Fig. 3(a)] or gating power [Fig. 3(e)]. By fitting each line with a Lorentzian function, we obtain a constant transition energy for different resonant powers [Fig. 3(b)], and observe a pronounced power-broadening [Fig. 3(c)]. Meanwhile, the RF intensity displays an unconventional power dependence characterized by an unexpected drop at $\sim$3 P0, as shown in Fig. 3(d), where P${}_{0}=1.15\pm 0.39$ $\mu$W is the resonant saturation power, determined by employing a pulse measurement scheme GeV . The drop of RF verifies the existence of dark state, and indicates the opposite role played by the resonant laser to the gating beam, i.e., shelving the population into the dark state.

As the gating power increases, the initially irresolvable PLE spectrum starts to recover and then stabilizes at $\sim$10*-5* P1 [Fig. 3(e)]. Through the evolution, the transition shows an exceptional stability by displaying zero drift of transition energy [Fig. 3(f)], and an unvarying excitation linewidth [Fig. 3(g)]. This superior optical property stems from the inversion symmetry of GeV center Siyushev et al. (2017), and shows a striking contrast to the significant spectral diffusion displayed by NV centers under non-resonant excitation Wolters et al. (2013). The slightly broadening of linewidth for the low gating powers ($<10^{-6}$ P1) is caused by the detuning dependence of shelving efficiency. Since the shelving becomes significantly stronger for smaller detuning (given a constant de-shelving rate), it causes a flattening of PLE spectrum, and gives rise to a wider linewidth GeV . This is similar to the linewidth broadening observed in SiV center at milli-kelvin temperature, where spin pumping plays the role of shelving Becker et al. (2018). As the gating power increases, the gating-based dynamics is enhanced and finally dominates over the resonant-induced shelving process, thus restoring the linewidth to its intrinsic value. When the gating power exceeds 10*-3* P1, the RF intensity starts to drop, which is accompanied by a rising of PLE background produced by non-resonant excitation [Fig.3(h)]. This reveals a competition between the resonant and non-resonant excitation.

The shelving effect induced by the resonant laser can be directly observed by modulating the resonant beam while keeping the non-resonant beam in cw-mode, as shown in Fig. 4(a). The immediate exponential decay of RF following the excitation edge directly monitors the shelving process. The hight of the transient peak reflects the population in the excited state before it is influenced by the shelving process induced by the resonant pumping. The subsequent plateau corresponds to the equilibrium state of the system dictated by both shelving and de-shelving rates. Following this phenomenological picture, we construct a 3-state model composed of a 2-level system and a dark state, as shown in Fig. 4(b). The population in the ground state (G) can be resonantly promoted ($\Omega$) to the excited state (E), where the population can either relax back to the ground state via spontaneous decay ($\Gamma_{\text{sp}}$), or be shelved into a dark state (D) non-radiatively ($k_{\text{ED}}$) via resonant pumping. The ground and dark state can exchange the population at rates $k_{\text{DG}}$ and $k_{\text{GD}}$, mainly enabled by non-resonant pumping. Within the framework of semi-classical picture, the time-evolution of the system follows the master equation

[TABLE]

where $\rho_{\text{G}}$, $\rho_{\text{E}}$, and $\rho_{\text{D}}$ are the time-dependent population in ground, excited and dark state, $\rho_{\text{GE}}$ and $\rho_{\text{GE}}$ are the coherence between G and E, $\Omega$ is the resonant Rabi frequency, $\Gamma_{\text{sp}}$ is the spontaneous decay rate, and $\text{T}_{2}$ is the coherence time of excited state. The excitation linewidth can be derived from the steady-state solution of Eqn. 2

[TABLE]

in the unit of linear frequency. By equalizing the asymptotic linewidth at 0 P0 in Fig. 3(c) ($\sim$1 GHz, 20 times of lifetime-limited value) to Eqn. 14 with $\Omega=0$, we find $\text{T}_{2}=316\pm 20$ ps, consistent with the coherence time obtained from Rabi oscillation measurement [Fig. 2(d)]. The detected RF intensity follows

[TABLE]

where $\eta=9\times 10^{-5}$ is the overall efficiency including both detection efficiency of the experimental setup and quantum yield of GeV center GeV ; Boldyrev et al. (2018).

To extract the dynamical rates of gating and shelving, we perform a similar time-resolved experiment, but modulating the non-resonant beam while keeping the resonant beam in cw mode. Here, the PL inherits the modulation pattern of the gating laser, and displays a gating-power-dependent modulation depth, as shown in Fig. 4(c). Since the non-resonant laser has little effect on $k_{\text{ED}}$, we keep this rate a constant and determine it via global fitting GeV . The main effect of the gating beam is to promote $k_{\text{GD}}$ and $k_{\text{DG}}$ linearly over the non-resonant power, as show in Fig. 4(d). This power dependence implies a single-photon process for the shelving and deshelving of population induced by the non-resonant laser. Consequentially, the steady-state population is transfered from the dark state to the ground and excited states as increasing the gating power, as shown in Fig. 4(e).

Resonant power dependence is shown in Fig. 4(f). The main effect of the resonant laser is to speed up the shelving rate $k_{\text{ED}}$, while indirectly reducing rates $k_{\text{GD}}$ and $k_{\text{DG}}$, as shown in Fig. 4(g). The saturation behavior of $k_{\text{ED}}$ implies a two-step shelving process mediated by a meta-stable state. The first step of population pumping from the excited state to the meta-stable state is responsible for the enhancement of $k_{\text{ED}}$, while the second step of non-radiative decay from the metastable state to the dark state caps $k_{\text{ED}}$ at kHz regime. The peak of steady-state population $\rho_{\text{E}}^{\infty}$ at several P0 in Fig. 4(h) suggests the optimal resonant power for the maximum RF given a gating power.

Now we briefly discuss the photophysics of the GeV system by comparing it to NV centers in diamond Fu et al. (2010); Waldherr et al. (2011) and InGaAs self-assembled quantum dots (QD) Nguyen et al. (2012); Chen et al. (2016), where a similar phenomenon has been observed. For both systems, the dark state has been identified as a differently charged species of the emitter, specifically, positively charged QD Nguyen et al. (2013) and neutrally charged NV center Aslam et al. (2013). It is hence plausible that the dark state of the GeV center is also a differently charged state (i.e., neutral) Thiering and Gali (2018). For all three systems, the gating of RF can be achieved by employing a small amount of non-resonant beam. The mechanism for NV centers and QDs involves a local free-charge-carrier bath produced by the light, which can modify the charge dynamics of the emitter in favor of resonant excitation. We argue a similar mechanism for GeV center as long as non-resonant laser is employed. The linear power dependence of $k_{\text{DG}}$ and $k_{\text{GD}}$ [Fig. 4(d)] also supports this argument. On the other hand, the shelving mechanism induced by resonant pumping is different. For QDs, no such a shelving channel is reported. For NV centers, a two-photon process is involved based on the quadratic power dependence of the dynamical rates Waldherr et al. (2011); Siyushev et al. (2013). For GeV center, a two-step shelving mechanism pivot by a meta-stable state and non-radiative decay channel is identified in this Letter. Finally, the decrease of rates $k_{\text{GD}}$ and $k_{\text{DG}}$ in Fig. 4(g) is possibly related to the decrease of free charge carrier density, caused by the presence of more charge traps in the area as induced by a stronger resonant beam GeV .

In summary, we demonstrated the shelving effect induced by the resonant laser in GeV centers, which can be counteracted by introducing a weak non-resonant repumping laser. The dynamics of shelving and gating can be quantitatively explained by the presence of a dark state, while the identity of this dark state warrants future investigation. We stress that this gating phenomenon is quite general and ubiquitous, not limited to the center investigated in this Letter GeV . The recovery and stabilization of the RF could be useful for quantum information science and scalable quantum photonics, such as spin-photon entanglement Togan et al. (2010); De Greve et al. (2012) and photon photon interferences Sipahigil et al. (2014).