Tunable phononic coupling in excitonic quantum emitters

Engineering the coupling between fundamental quantum excitations is at the heart of quantum science and technologies. A significant case is the creation of quantum light sources in which coupling between single photons and phonons can be controlled and harnessed to enable quantum information transduction. Here, we report the deterministic creation of quantum emitters featuring highly tunable coupling between excitons and phonons. The quantum emitters are formed in strain-induced quantum dots created in homobilayer semiconductor WSe2. The colocalization of quantum confined interlayer excitons and THz interlayer breathing mode phonons, which directly modulate the exciton energy, leads to a uniquely strong phonon coupling to single-photon emission. The single-photon spectrum of interlayer exciton emission features a single-photon purity>83% and multiple phonon replicas, each heralding the creation of a phonon Fock state in the quantum emitter. Owing to the vertical dipole moment of the interlayer exciton, the phonon-photon interaction is electrically tunable in a wide range, promising to reach the strong coupling regime. Our result demonstrates a new type of solid-state quantum excitonic-optomechanical system at the atomic interface that emits flying photonic qubits coupled with stationary phonons, which could be exploited for quantum transduction and interconnection.


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The quantized vibrational motion in solid-state quantum systems, i.e., phonons, has been exploited as an important modality that interfaces with electrons and photons for quantum information science and applications 1,2 . In bulk diamond, the optical phonon with a frequency of 40 THz has been mapped to Raman scattered photons to realize non-local entanglement at room temperature [3][4][5] . In microscopic cavity optomechanical systems, phonons of MHz to GHz frequencies have been used to store and transfer quantum states between microwave and optical photons 6,7 . In molecular quantum emitters, coupling with the phonons of the host medium is generally considered detrimental to the quantum properties 8 , although the molecule's internal optomechanical degree of freedom has been exploited 9,10 . These archetypical demonstrations utilize either bulk phonon modes involving collective vibration of many atoms or a phonon band including a large number of unresolved modes, resulting in a relatively low phonon-photon scattering probability or coupling rate. To further explore the phonon degree of freedom in the quantum regime, therefore, it is highly desirable to engineer new quantum light sources that afford strong phonon-photon coupling involving a well-defined single phonon mode, preferably with an intermediate high frequency and tunable coupling strength.
Quantum emitters (QEs) in two-dimensional materials 11,12 , including transition metal dichalcogenide (TMDs), hexagonal boron nitride (h-BN), and their heterostructures, provide new opportunities for engineering quantum-regime phonon-photon coupling. These atomically-thin materials have bright exciton emissions and are very rich in optically (Raman) active phonon modes [13][14][15][16] . Their multilayers further afford intralayer and interlayer phonons with a vast span of frequencies from optical to acoustic ranges. Moreover, QEs in 2D materials can be deterministically created with several approaches, such as strain engineering and ion implantation [17][18][19] . These techniques have enabled the site-controlled creation of QEs with a high yield and high single-photon purities. Being hosted in atomically thin materials, 2D QEs are amenable to photonic integration to facilitate photon extraction 20 and Purcell effect enhancement of emission 21 , providing a versatile quantum system to explore phonon-photon interactions.
Here we report strong and tunable phonon-photon coupling in strain-engineered 2D QEs that are deterministically created in bilayer WSe2. These 2D QEs emit single photons with high purity and have a high electrical tunability in emission energy. Remarkably, in the single-photon emission spectra, multiple well-resolved phonon replica lines are observed, each of which heralds the creation of a phonon Fock state. The large phonon-photon coupling in this QE system stems 3 from the colocalization and quantum confinement of the interlayer excitons and the breathing mode phonons, which directly modulates the exciton energy. The very high phonon-photon coupling strength is characterized by a large and electrically tunable Huang-Rhys factor reaching the highest value realized in solid-state quantum emitter systems [22][23][24][25][26][27] . The demonstrated strong and tunable single phonon-photon coupling provides an invaluable resource for engineering quantum light emission systems with an additional internal mechanical degree of freedom for quantum information processing.
The bilayer WSe2 is an ideal system to explore the phonon-photon interaction as it affords many Raman-active phonon modes covering a broad frequency range 28,29 . Particularly, as shown in Fig. 1a, the interlayer breathing mode (BM) phonon couples with the interlayer excitons (IXs) strongly, as the electronic excitation of an IX with a vertical dipole moment is modulated directly by the interlayer vibrational state. To explore this coupling at the single-photon level, we use the strain-engineering approach to create QEs in bilayer WSe2 by transferring them onto patterned nanopillars 17,18,30 , as illustrated in Fig. 1a. The nanopillars induce local strain that modulates the bandgap and thus creates spatial confinement of IXs in the bilayer WSe2 31 , resulting in quantum dots with single-photon emission 32 . Fig. 1c illustrates the potential traps formed by the localized strain in the bilayer WSe2. The optically excited IXs are funneled into the traps where they are bound with natural defects and recombine to emit single photons. In comparison to excitons in monolayer TMDs that have no electric dipole moment, IXs in bilayer WSe2 have a large out-ofplane electric dipole moment 29,[33][34][35] . Therefore, they couple efficiently to both a perpendicular electric field that generates a Stark shift and the interlayer vibration. Stark shifts of the IX energy by more than 50 meV has been achieved in bilayer WSe2 and other TMDs 36,37 . Multiple QEs can be created at each site in the nano-pillar array (Fig. 1b). While the QEs at different sites have different emission energy due to the variation of the local parameters such as the amount of strain and the energy level of the defects, applying a local electric field to each of them using separate gate electrodes can tune their emission energies to be the same.  Fig. 1e shows the density functional theory calculated band structure of bilayer WSe2 in its pristine state and strained state with 1% tensile strain. In 4 pristine bilayer WSe2, indirect bandgap transition Q-K can occur, assisted by various singlephonon or two-phonon processes 29 . When under a sufficient amount of strain, the conduction band minimum is shifted from the Q point to the K point, and the valance band Γ point is shifted up such that direct K-K and indirect K-Γ transitions can become favorable in energy, enabling strong exciton coupling to zero-momentum phonons 29,[38][39][40][41] . Therefore, depending on the level of local strain, IX species corresponding to either Q-K, K-Γ, or K-K transitions can dominate the photon emission. These IX species have different dipole moments 35 , but because their energy is susceptible to the interlayer separation, they all couple to BM phonon strongly.

Tunable quantum emitters
We fabricated multiple samples. In each sample, we can find multiple QEs at different nanopillars in the array. All the measurements were performed in a cryostat at a temperature of 10 K. This turn-on behavior may be attributed to the IXs being bound to a donor (or acceptor) type defect that electron (or hole) doping is needed for IX to bound to the defect and form a QE. Both donor and acceptor type defects in WSe2 has been reported previously 42  previously reported experimental results, which type of IX dominates the QE depends on the local 5 strain level 29,35,38,[43][44][45][46] . Because the local strain level can vary a lot at each nanopillar and the formation of QEs is by the accidental occurrence of a proper defect, the strain levels at different QEs can be very different, thereby leading to different types of IX. Even higher tunability can be achieved with QEs in heterobilayers, such as moiré excitons 47 , which have an even larger dipole moment. Fig. 2c shows the PL spectra of another QE (QE2), which behaves differently from IX QEs. QE2 is bright at zero gate voltage with an emission energy of 1550 meV, which remains unchanged with varying gate voltage until 3.0 V when the emission is turned off. This type of QE can be attributed to defect-bound intralayer excitons, which do not couple to the out-of-plane electric field and are rarer (only three out of 22 QEs we measured). However, a sufficiently high electric field can cause electron or hole tunneling to another layer of WSe2, consequently turning off the intralayer exciton emission.
The two types of QEs' different responses to electrical modulation allow us to tune them to the same energy, as summarized in Fig. 2e. In Fig. 2b and d, when gate voltages of -5.0 V and 2.0 V are applied to QE1 and QE2, respectively, both QEs emit photons at 1550 meV with similar linewidths. Fig. 2f shows the second-order photon correlation g (2) () measured from a device (QE13 in Supplementary Information) behaving similarly to QE1. A filter with ~5.0 nm (9.7 meV) bandwidth was used to select the measurement range. The result shows clear antibunching with g (2) (0)=0.169±0.005, indicating single-photon purity of 83%. From fitting the autocorrelation data, we estimate the QE lifetime to be 2.0±0.25 ns. We have measured similar antibunching results from many QEs with linewidths in the range of 1 to 3 meV across different devices, which are included in the Supplementary Information. The demonstrated wide electrical tuning range makes these 2D QEs promising for achieving scalable arrays of indistinguishable single-photon sources.
In areas without nanopillars, we measure IX emission with a much broader linewidth > 5 meV and without antibunching, which is consistent with previous reports 29,33,35,48 . Also, we observed no pronounced emission in a wide energy range below the bandgap (Supplementary Figure 13), emission due to in-gap defect states can be ruled out. Therefore, we conclude that the combination of defect and strain engineering is necessary to create the QEs 30 . There are several possible types of defects in WSe2, including Se vacancy, W anti-site, O-passivated Se vacancies, and O interstitials 32,[49][50][51][52] . Although which type of defect is responsible for forming the QE is unclear, requiring microscopic study to reveal, the Se vacancy has a higher density than other types so is more likely to occur at the nanopillars. 6

Single exciton-phonon coupling
A very notable feature in the PL spectra of QE1 (Fig. 2a) is multiple emission lines on both sides of the main peak. These emission lines are turned on/off by the gate voltage along with the main peak and modulated at the same rate, suggesting their correlation. We observed similar features in many devices. Figs. 3a and b show the PL spectra of QE1 and another QE (QE3), measured with gate voltages of -6.4 V and -5.0 V, respectively. Five emission lines can be observed with spacings in the range of 3.0-3.7 meV for QE1 (Fig. 3a), and 3.7-5.1 meV for QE3 (Fig. 3b). We then and f show that the energies of these lines are tuned by the gate voltage synchronously at the same rate, with their spacings unchanged. All these features allow us to conclude that these emission lines originate from the same QE, rather than other emitters nearby.
The observation of multiple well-resolved emission lines can be explained as phonon replicas due to the coupling between colocalized single IX and a single phonon mode in the QE.
Their coupling can be understood with the Franck-Condon principle, as illustrated in Fig. 4a 26,27,[53][54][55] . The ground state of the QE and its excited state when an IX is generated can be modeled with two potential energy surfaces (PES). Each PES is populated with phonon states that are not evenly spaced because of the anharmonicity of the PES. Under the linear coupling approximation, the phonon-exciton coupling is represented by a shifted equilibrium position of the excited-state PES relative to the ground-state. At low temperatures, the QE at the ground state PES has nearly zero phonon occupancy. When an exciton is created by the pump laser, the QE is excited into higherenergy PES and quickly relaxes to its zero phonon level. Upon exciton recombination, the QE emits a single photon and relaxes to its ground-state PES but at an elevated phonon state (Fig. 4a).
As a result, the energy of the emitted photon is Stokes-shifted from the zero-phonon line (ZPL), forming phonon replicas spaced by the phonon energy. In Fig. 4a, the emission lines are labeled with the corresponding phonon number state |n in the ground state PES. According to the Huang-Rhys theory for discrete phonon lines, the intensity of the n th phonon line is proportional the overlap integral between the initial and final phonon states, i.e., |⟨0| ⟩| 2 = − / !, where S is the dimensionless Huang-Rhys factor measuring the strength of the exciton-phonon coupling 56 .
Therefore, the phonon line intensities have a Poisson distribution with an expectation value of S, 7 as illustrated in Fig. 4a. In many other solid-state QEs, such as the color centers in the diamond, the coupling of defect emitters to bulk phonons produces phonon sidebands that are not well resolved due to the continuous phonon DOS in energy. In contrast, in Figs first-principle theory to be ~0.026 Å. g 0 is zero-field coupling rate, which is calculated to be <0.08 meV, one order of magnitude smaller than the second term when the field is strong. Thus, assuming that the applied field can reach a reasonably high value of 0.25 V/nm in our device 59 , 0 can be increased to 1.3 meV. The system thus can reach the strong-coupling regime, satisfying 2 0 > ( , ), where ~1.17 meV is the exciton linewidth (Fig. 2b) and <1.18 meV is the BM phonon decoherence rate given its coherence time of 3.5 ps measured at room temperature 36,37,59 . At cryogenic temperatures and with better sample quality, we expect and can be further reduced.

Conclusion
We have created highly tunable QEs in WSe2 bilayers with strain engineering methods. An immediate next step is to integrate these emitters with integrated photonic platforms such as waveguides and photonic crystal cavities to achieve super-radiant emission, Purcell enhancement, and cavity QED. With twisted bilayer WSe2 rather than a natural bilayer, the IX energy can be tuned electrically while still maintaining the characteristic valley states similar to those reported in moiré systems 36,37,60 . Furthermore, the demonstrated tunable phonon-photon coupling strength in these 2D QEs provides a new way to explore the quantum optomechanical effects. In many ways, the 2D QEs are analogous to cavity optomechanical systems, but at the atomic interface and with a phonon frequency of 0.8-1.0 THz, which is already at the ground state at the measurement temperature of 10 K. It will be possible to use a THz source to resonantly excite the phonon and prepare phonon Fock states in such a solid-state system at a temperature higher than ever before. 9 The archetypical excitonic-optomechanical system demonstrated here thus has the potential to be a new quantum light resource that is entangled with single phonons 1,2,60,61 for use in quantum information processing, storage, and communication 1,2,61,62 . After the device has been transferred, contact electrodes of Ti/Au to the graphite were patterned with photolithography using a direct laser writer and deposition using electron beam evaporation.

Device Fabrication:
An optical image of a device is shown in Fig. 1d, where the strain induced by the nanopillars is visible.
Photoluminescence measurement method: The sample was wire bonded to a sample holder and loaded into a cryostat (Montana Cyrostation S-100) to be cooled to 10K for measurement. A leakage test was done to ensure that the electrodes are not shorted together, and then the photoluminescence spectra of strained heterostructure can be measured at different bias voltages.
A continuous-wave He-Ne laser (632.8nm) was used to excite the excitons. The laser beam was focused on the sample through an optical window in the cryostat with a 50 objective lens (NA = 0.42) to achieve a diffraction-limited spot size of about 1 m in diameter. The interlayer exciton emission was passed through a 633 nm notch filter to remove the reflected signal of the laser before being acquired with a spectrometer (Princeton Instruments, IsoPlane 320).

Data availability statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.