Polarization Dynamics of Solid-State Quantum Emitters

Abstract

Quantum emitters in solid-state crystals have recently attracted a great deal of attention due to their simple applicability in optical quantum technologies. The polarization of single photons generated by quantum emitters is one of the key parameters that plays a crucial role in various applications, such as quantum computation, which uses the indistinguishability of photons. However, the degree of single-photon polarization is typically quantified using the time-averaged photoluminescence intensity of single emitters, which provides limited information about the dipole properties in solids. In this work, we use single defects in hexagonal boron nitride and nanodiamond as efficient room-temperature single-photon sources to reveal the origin and temporal evolution of the dipole orientation in solid-state quantum emitters. The angles of the excitation and emission dipoles relative to the crystal axes were determined experimentally and then calculated using density functional theory, which resulted in characteristic angles for every specific defect that can be used as an efficient tool for defect identification and understanding their atomic structure. Moreover, the temporal polarization dynamics revealed a strongly modified linear polarization visibility that depends on the excited-state decay time of the individual excitation. This effect can potentially be traced back to the excitation of excess charges in the local crystal environment. Understanding such hidden time-dependent mechanisms can further improve the performance of polarization-sensitive experiments, particularly that for quantum communication with single-photon emitters.

Keywords: defect identification; density functional theory; electron irradiation; hexagonal boron nitride; nanodiamond NV centers; quantum emitters array; temporal polarization dynamics.

Figure 1

(a) Optical microscope image of the exfoliated hBN flake on a Si/SiO₂ substrate. (b) PL map of the irradiated array, excited with a 530 nm pulsed laser at a repetition rate of 20 MHz. The inset image is a zoomed-in PL map of one of the irradiated spots, revealing multiple single-emitter spots. (c) Typical spectrum of a single emitter with a peak of the PL at 575 nm, detected with a long-pass filter at 550 nm, that cuts the emission partially. The inset figure shows the typical lifetime decay curve, revealing a lifetime of 3.97(7) ns. (d) The second-order correlation function under pulsed excitation at the position marked “x₁” in (b) with g²(0) = 0.017(3) and at “x₂” with g²(0) = 0.042(2). The g²(0) values were extracted from the fitted curve.

Figure 2

(a) PL map of the entire flake created using a pulsed excitation laser at 530 nm. The emission and excitation axes of the measured emitters are presented with arrows at the measured angle relative to the (random) x-axis, as marked in the map. One of the main crystal axes had an angle of 43.52° ± 0.39° with respect to the x-axis. (b) A typical polar plot of the emission and excitation axes at the spot marked with a white “▼” in (a). The degree of polarization was extracted from a cosine-squared fit with 98.01% (emission) and 96.67% (excitation). Here, the red and blue grid lines present the crystal axis in order to correlate the emission and excitation axes with respect to the crystal axis. (c) The polarization-resolved SHG measurements revealed the crystallographic axes, as evident by the 6-fold symmetry. These axes are also marked in all subplots. Scatter plots of the measured (d) excitation and (e) emission axes against the degree of polarization of the emitters. All of the emitters presented in the scatter plots have a clear g²(τ = 0) dip and an average lifetime of around 4 ns, as indicated in the plot. (f) The misalignment between the excitation and emission axes of polarization with a mean value of 18.9(100)°. (g) Emission versus excitation axes showing a linear behavior. The plot shows a clear splitting into two groups identified as “Set-1” and “Set-2”, which both have a slope of nearly 1.

Figure 3

(a) The PL intensity with respect to time after the excitation laser pulse as a function of the polarizer rotation angle measured for (a₁) hBN irradiated QEs, (a₂) hBN nanoflake QEs (with g²(τ = 0) values well below 0.5), and (a₃) NV center ensembles in diamond (with g²(τ = 0) above 0.5). The dashed lines represent the extracted lifetime of the emitter. (b) The variation of the linear degree of polarization and (c) the axis of polarization measured with respect to time slices (time spent in the excited state) for different emitters. The dashed lines indicate the time-averaged visibility and polarization axis obtained by integrating over an extended time period (i.e., the results observed in Figure 2). For the irradiated hBN emitters and NV centers, measurements were obtained with a pulsed excitation of 530 nm at 20 and 10 MHz repetition rates, respectively. Measurements for the hBN nanoflake emitters were obtained under 483 nm pulsed excitation at a 10 MHz repetition rate.

Figure 4

(a) Potential energy surface of a neutral-charged C₂C₂ defect without strain, representing the complete excitation and emission process, consisting of the absorption (green line), the zero-phonon line (ZPL, yellow line, here 573 nm), and the phonon sideband (PSB, magenta line). (b–d) The probability density |ψ|² of electron occupations in the ground state at point 1 and in excited states at points 2 and 3, respectively. (e) The charge difference between points 1 and 2 is shown by the isosurfaces, where the green arrow indicates the excitation dipole axis with light radiation in green shade. The excitation axis makes a 11.1° angle relative to the crystal axis (red dashed line). (f) The charge difference between points 1 and 3 with the yellow arrow indicating the emission dipole axis with light radiation in yellow shade. The emission axis makes a 12.1° angle relative to the crystal axis.