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Advances are being made in an effort to fulfill the promise of solid state quantum computation,¹ yet there remains a need for sophisticated single spin manipulation and measurement techniques. While there has been substantial progress with both electrical^2,3 and optical⁴ methods, it is important to develop schemes for implementing and integrating these protocols at room temperature. Photonic cavities provide a flexible platform to increase the sensitivity of optical measurements, as well as the possibility to study emergent light-matter interactions.^5,6 The application of a simple multiple pass sample cell to increase sensitivity in optical techniques has existed for decades.⁷ Recently, dielectric Bragg reflector (DBR) cavities have been exploited to investigate Faraday rotation in magnetic layers,⁸ imaging of domains in dilute magnetic semiconductors,⁹ and time-resolved measurements in quantum wells.¹⁰ Many of these structures are based on an all molecular beam epitaxy fabrication approach.¹¹

In this letter, we describe a generic platform that enhances the Faraday rotation (FR) of molecularly self-assembled colloidal CdSe quantum dots (QDs). With these chemically synthesized materials embedded in a dielectric vertical cavity, we use time-resolved Faraday rotation (TRFR) to investigate spin dynamics and coherence of the QD films. By independently controlling the pump and probe wavelengths, we systematically assess the role of the cavity in the resulting enhanced signal. More than an order of magnitude increase in the FR angle is observed in the cavity as compared to control samples. We find that the g factors of the QDs remain unaffected by introduction into the cavity. The increase in detection sensitivity allows the systematic investigation of spin dynamics to pump power densities of 0.5  mW/cm², where we find that the contributions to spin precession are largely power dependent. This scheme could be incorporated into a host of systems (fluctuation QDs, planar devices, etc.) as a generic approach to increase the signal to noise ratio in FR measurements without perturbing the intrinsic properties of the system under investigation.

Fabrication of the DBR cavity begins with the electron beam evaporation of 5.5 pairs of TiO₂/SiO₂ quarter-wavelength layers deposited on a 1  mm thick glass substrate. Next, the sample is capped with a thin SiO₂ layer to position a suitable surface for the molecular-assembly of QDs in the center of the completed cavity. This SiO₂ surface is functionalized by immersing the sample into a 1  mM solution of 1,4-dihexyloxy-2,5-bis[4-thiolstyry]benzene (Ref. 12) in toluene for 2–4  h. This molecule contains two thiol functionalities for chemically binding CdSe QDs, and similar compounds have previously been used to fabricate and test metal-molecule-metal junctions.¹³ The CdSe QD (6.6  nm diameter) layer is assembled by soaking the modified substrate in a QD solution for 13–16  h.¹⁴ The same molecular self-assembly procedures are repeated a few times until a sufficiently high optical density (OD=0.01) is obtained. This assembly protocol allows the OD of each sample to be varied by adjusting the number of deposition cycles. For this study we have created one sample with high OD (sample A) and one with low OD (sample B), vide infra. These modified samples were subsequently coated with a wedge-shaped SiO₂ layer to tune the half-wavelength layer, and therefore the cavity mode resonance continuously. Finally, a second TiO₂/SiO₂ DBR that is identical to the first series of depositions is evaporated to complete the cavity structure as can be seen by the electron microscopy cross sections in Fig. 1(a). The inset shows that the film consists of 1–3 layers of QDs.

Figure 1.

In order to assess the role of the cavity, it is critical to compare the response of the identical film inside and outside the structure. This is achieved by dividing each substrate into a cavity region and a control region. The control side is masked during depositions of the bottom and top DBRs, whereas the whole substrate is exposed to the QD assembly protocol. In order to ensure that the films are identical, a thin layer of SiO₂ is deposited in the control region before and after QD deposition. This procedure allows for quantitative comparison between the film in the cavity versus the control. Shown in Fig. 1(b) are the optical absorption spectra of the control region of both samples (A and B). The first exciton absorption (1S_e–1S_3/2 transistion) appears at 625  nm in both films and a reference solution of QDs in toluene. The linker molecules used in the assembly process do not have absorption for 450  nm.¹²

In the cavity structures, a single DBR typically has a maximum reflectivity of 96% at the center wavelength (685  nm) and stop band edges of 550 and 800  nm. The refractive indices for SiO₂ and TiO₂ layers are estimated to be 1.46 and 2.07, respectively. Using existing analysis,¹⁵ we find the phase penetration depth to be 270  nm. Optical characteristics of a complete cavity are shown in Fig. 1(c). The transmission spectra of four different positions of sample A demonstrate that the cavity mode can be tuned from 595  to  630  nm. The inset shows the width of the resonance and its fit to a Lorentzian line shape. A similar analysis is conducted for sample B in Fig. 1(d). Here the cavity mode can be tuned from 600  to  635  nm and has a higher Q due to reduced absorption from the embedded QDs. When these cavities are compared to similar structures without the QD layer, the maximum transmission at a cavity mode increases from 54% to 80%. The reduction in transmission from a loaded cavity can be largely attributed to the enhanced absorbtion. However, the Q factors are similar implying that a high quality interface persists on both sides of the QD layer despite the vast change in surface chemistry.

We measure coherent spin dynamics by time-resolved Faraday rotation in the Voigt geometry.¹⁶ A regeneratively amplified Ti:sapphire laser pumps two optical parametric amplifiers to produce a pair of synchronized independently tunable optical pulses of 200  fs duration (pump and probe with wavelengths _pump and _probe, respectively). The helicity of the circularly polarized pump beam is varied by a photoelastic modulator at 42  kHz, whereas the linearly polarized probe beam is mechanically chopped at a frequency of 390  Hz. At room temperature, these pulses are focused to a 100  µm spot on the sample which resides between two permanent magnets used to apply a field of 0.47  T perpendicular to the pump and probe directions. The magnetization and subsequent precession of the excited carriers result in the rotation of the linear polarization of the probe. The relative time delay between the pump-probe pulses is adjusted by a mechanical delay line. Probe powers are typically 1  mW/cm² and all results were independent of probe intensity.

A typical TRFR scan of sample A with a cavity resonance of 630  nm, P_pump=40  mW/cm², and _pump=560  nm is plotted in Fig. 2(a). The signal from the cavity is signifigantly larger than that of the control measured under the same conditions. Since _pump is below the stop band edge, the low reflectivity of the DBRs makes any effect from the cavity on the pump beam negligible. Hence, the enhancement observed here can be solely attributed to the cavity's effect on the resonant probe beam. To quantitatively assess our samples, we fit the TRFR data to the following equation:

where t is the delay time of the pump pulse, ₁ (₂) is the amplitude of the first (second) spin precession component, T (T) is the transverse spin coherence time, ₁ (₂) is the Larmor frequency, ₁ (₂) is the phase, ₀ and t₀ are the amplitude and decay time constant, respectively, for the nonoscillating background, and _C is the offset. Analysis of sample A yields ₁=0.12  mrad and ₂=0.55  mrad for the cavity at a resonance of 630  nm. In contrast, the two FR amplitudes for the control are found to be ₁=0.011  mrad and ₂=0.046  mrad. The Larmor frequencies are found to be ₁=7.8  GHz and ₂=10.8  GHz, corresponding to g factors g₁=1.18 and g₂=1.64, respectively. The dephasing times T and T are found to be approximately 100 and 250  ps, respectively.¹⁷ We find no discernible difference between g factors of the cavity and the control. The origin of the two distinct components of FR oscillations has previously been attributed to exciton (₁,T₂₁) and electron (₂,T₂₂) precessions and that picture will be adopted here.^18,19 The important difference between the control and the cavity resides in the increased FR signal.

Figure 2.

In order to quantify the increase in Faraday rotation we define an enhancement factor using coefficients from Eq. (1). Since the amplitude associated with the electron Larmor frequency is small for the control region, we use the ratio between the sums of the two FR amplitudes to calculate the cavity enhancement factor, i.e., F_enhc=(₁+₂)_cavity/(₁+₂)_control. Averaging of the scans over at least five positions in the control and two in the cavity yields F_enhc=12±1 for sample A and F_enhc=20±2 for sample B at a 630  nm resonance. To further explore this, we made measurements as a function of position on both cavities. This allows for the dependence of F_enhc on the resulting quality factor to be determined. Measurements with probe wavelengths between 620 and 625  nm are avoided because the signal from the control is quite weak and FR oscillations vanish near the peak of the 1S_e–1S_3/2 transition. As can be seen in Fig. 2(c) the enhancement is dependent on the quality factor, and in our case, an increase of more than 25 times is achievable.

This phenomenon can be explained by considering how the probe beam interacts with the cavity, and subsequently, the QDs. One way to view this type of cavity structure is that multiple passes of the probe beam within the cavity amplify the absorbance, and subsequently, the Faraday rotation. Alternatively, an optical localization picture can be adopted where interference effects lead to cancellation and amplification of the optical field. This produces an electric field antinode at the center of the cavity, and thus an enhanced interaction between the probe beam photons and the QDs placed at or near this maximum. In these large mode volume cavities with photon lifetimes of less than 1  ps, we expect a linear increase of F_enhc with Q. The data shown in Fig. 2(c) qualitatively agree with this picture. However, a quantitative comparison is complicated by experimental factors such as variation in QD density, position of the film relative to the antinode, dielectric uniformity, etc.

The cavity enhancement can be used to study QDs at extremely low pump and probe power levels. As shown in Fig. 3(a), the spin dynamics at low pump power (2.0  mW/cm²) are quite different from higher power in that the beating of FR oscillations is much stronger at low power. In Fig. 3(b), fast Fourier transforms (FFTs) of time-domain TRFR data reveal that the relative weight of the low frequency component is greater at lower power and the g factors are independent of pump power. Once again, fitting the FR data with Eq. (1) demonstrates that the two precession components of FR vary as a function of pump power (P_pump).¹⁷ As can be seen in Fig. 3(c), both ₁ and ₂ increase with P_pump, but the low frequency component ₁ begins to saturate much faster than ₂. Qualitatively similar results were observed for various _pump and _probe conditions.

Figure 3.

Previous studies have probed large numbers of QDs either in polymer glasses¹⁸ or thick densely packed films.¹⁹ Using both electron microscopy and optical absorbance, we find that our films have a density of 1.3×10¹²  QDs/cm² and correspondingly we probe 9×10⁸ QDs. If we assume signal levels observed in our control films as a lower bound and reduce our spot size with a high numerical objective, we conservatively estimate the current detection limit of Faraday rotation to be 3×10⁴ QDs using this cavity.

In conclusion, we have demonstrated a flexible platform to increase the sensitivity of ultrafast spin dynamics measurements. We have established that this design is compatible with chemically synthesized materials systems and may prove useful as molecules begin to play an increasingly important role in spintronics. Finally, we take advantage of the cavity enhanced signal to show that contributions to FR are pump power dependent in CdSe QDs. Single spin detection may be within experimental reach with the application of this cavity structure to other quantum confined spin systems.

The authors acknowledge Dr. J. Löfvander for TEM/FIB assistance and support from ONR, and NSF.