The Dalian Institute of Chemical of the Chinese Academy of Sciences realizes the room-temperature coherent manipulation of colloidal quantum dot spin

On December 20, 2022, Beijing time, Wu Kaifeng’s team from the Dalian Institute of Chemical Physics, Chinese Academy of Sciences published a research result entitled “Room-temperature coherent optical manipulation of hole spins in solution-grown perovskite quantum dots” in the journal Nature Nanotechnology.

The research team is the first in the world to realize the ultrafast coherent manipulation of colloidal quantum dot spins prepared by low-cost solution method at room temperature, which is of great significance in the fields of quantum information science and ultrafast optical coherent manipulation.

The corresponding author of the paper is researcher Wu Kaifeng, and the co-first authors are doctoral students Lin Xuyang and Dr. Han Yaoyao.

Coherent manipulation of spin qubits in solid materials is one of the important ways to realize quantum information technology. Compared to bulk semiconductor materials, confined domain materials, such as epitaxial growth quantum dots, have the advantage of manipulating and addressing individual spins. Therefore, the researchers believe that they are more suitable for quantum information science. Other confined systems include defect centers in solids, which can generally be manipulated using electric or magnetic pulses at microwave frequencies for spin quantum states, but on the fastest timescales in the nanosecond range.

Although the above spin manipulation methods have achieved certain results, from the perspective of practical application, there are still many shortcomings in the carrier materials of spin. The preparation of epitaxial growth quantum dots usually requires the use of high temperature and high vacuum conditions, so the cost is high. In addition, at a fundamental level, scattering between energy levels and coupling of phonons causes spin to dephase rapidly. Therefore, spin manipulation of epitaxial growth quantum dots needs to be performed at liquid helium temperature (a few kelvins). In contrast, the spin of defective or doped centers in solids is highly localized and can be manipulated by spin at room temperature, but large-scale preparation of such spin materials is difficult. Therefore, the development of spin carrier materials that can be manipulated at room temperature and low cost is of great significance to realize the large-scale application of spin quantum information technology.

Colloidal quantum dots (QDs), also known as nanocrystals, can be prepared on a large scale in solution at low cost; At the same time, its morphology and size can be precisely controlled, especially suitable for self-assembly or device integration. Considering that the spin manipulation of traditional colloidal CdSe QDs cannot be achieved at room temperature, the research group turned to focus on lead-halide perovskite QDs. Their spin-orbit coupling effect and electronic structure allow them to be optically injected with spin polarization, while their strong light-matter interaction facilitates spin manipulation through the optical Stark effect (OSE). However, the exciton room temperature spin lifetime of lead-halide perovskite QDs is very short (several picoseconds), so it is difficult to achieve their room temperature spin manipulation. The researchers speculate that enhanced electron-hole exchange in confined systems may be the dominant factor in inducing room temperature exciton spin relaxation.

Here, the research team combined the interfacial transfer chemistry and femtosecond pulses of lead-halide perovskites to initialize, manipulate, and read out hole spins at room temperature. After using anthraquinone (AQ) molecules to modify the surface of CsPbBr3 QDs, and using circularly polarized light to excite QDs, after generating spin-polarized excitons, AQ molecules can extract electrons on subpicosecond time scales, thereby releasing electron-hole exchange and preparing spin-polarized holes. Under the action of an applied transverse magnetic field, spin-polarized holes can precession around the external magnetic field for up to 100 picoseconds. At this point, by applying a second non-resonant laser pulse, the OSE effect is generated, and the hole spin can be rotated in the longitudinal axis. In summary, the research group successfully realized the manipulation of spin quantum states at room temperature by applying the OSE effect to the holes of spin precession under the external magnetic field.

Sample characterization as well as experimental setup

Figure 1: System design and experimental setup. (a) Absorption spectra of CsPbBr3 QD1 (solid purple line) and QD2 (solid blue line). The shadow pulses are the spectra of pump and tipping pulses. The arrows point to the central wavelength of the two lowest exciton peaks QD1 (violet) and QD2 (blue). (b) Band edge optical selection rules for CsPbBr3 quantum dots under quasiparticle images. Circularly polarized σ+, σ-photon selectively coupled to different optical transitions. (c) Diagram of the device for the spin manipulation experiment. OPA: optical parametric amplifier; BBO: barium borate crystals; QWP: quarter slides. (d) Study of different pulse train schemes for spin precession, optical Stark effect, and coherent spin manipulation.

Figure 1 shows sample characterization, optical path design, and experimental methods. All tests are performed at room temperature. CsPbBr3 QDs with controllable dimensions are synthesized by thermal injection. Figure 1a shows the absorption spectra of two QD samples (QD1 and QD2) dispersed in n-hexane. Among them, the lowest energy exciton peaks of QD1 and QD2 are located at 470 nm and 481 nm, respectively (Figure 1a). Compared with bulk materials, the confinement effect will lead to the quantization of the energy level of QDs, which is conducive to suppressing phonon-induced energy level scattering and prolonging the spin life. The research team modified QD using carboxyl-modified AQ molecules, a common electron acceptor. Through the energy level position and spectral characterization of CsPbBr3 QDs and AQ molecules, it is found that for QD1 and QD2, the process of QD transfer of electrons to AQ molecules occurs on subpicosecond time scales, and the subsequent generation of QD+-AQ-charge separated species has a lifetime of more than 10 ns.

Figure 1b shows the banded optical transition selection rule for CsPbBr3 QDs under quasiparticle images. Under cubic symmetry, the energy levels of the valence band (|s=1⁄2, ms=±1⁄2>) and the spin-orbital splitting energy levels of the conduction band (j=1⁄2, mj=1⁄2>) is optically coupled by circularly polarized (σ- and σ+, respectively). Shape anisotropy and anisotropic exchange due to lattice distortion may cause the circularly polarized exciton eigenstate to become a linearly polarized exciton eigenstate. However, from the OSE effect of circular polarization selection shown next in this paper, at least at room temperature, the circular polarization selection rule is still applicable. The research group mainly focuses on the spin of a single hole, where the exchange interaction has been eliminated.

In the optical test (Figure 1c), the research group used a femtosecond laser amplifier to pump the optical parametric amplifier to generate a wavelength-tunable pump pulse. The other part of the fundamental frequency light is multiplied through a BBO crystal to obtain a rotating pulse (Tipping light) with a wavelength of 515 nm. Figure 1a shows the spectra of pump light for QD1 and QD2, where the photon energy resonates with the lowest energy exciton absorption peak of QDs. Tipping photons have lower optical bandgaps with lower energies than QDs and act as non-resonant rotational pulses. A relatively weak beam of 515 nm light is focused onto a sapphire crystal to produce supercontinuous white light, which is then transformed into a circularly polarized detection pulse by polarizers and quarter waveplates. All three beams of light are focused on the sample placed on the quartz cuvette. A transverse magnetic field (Bz) is applied to the outside world, i.e. the Voigt configuration, where Pump light or Tipping light is modulated by a chopper, resulting in a change in absorbance (ΔA) detected by white light. Compared to the detection method of Faraday rotation used in previous literature, this method can record ΔA using various chopper modulations and immediately obtain a wideband signal.

Room temperature hole spin precession

Figure 2: Room temperature hole spin precession of CsPbBr3 quantum dots. (a) Diagram of the energy level when a transverse magnetic field (Bz) is applied. After transferring conduction band electrons using electron acceptors, valence band holes oscillate between (|↑>±|↓>)/√2, where |↑> and |↓> are the eigenstates quantized by the external magnetic field. (b) Hole spin precession Bloch ball. The z-axis is parallel to Bz. (c) Two-dimensional false-color transient absorption (TA) spectra of QD1-AQ in the (left) same circular polarization (σ+/σ+) and (right) opposite circular polarization (σ-/σ+) pumping/detection configurations at Bz = 0.65 T. (d) At the top, at 0.65 T, TA kinetics at 484 nm have opposite phases in the same circularly polarized (blue solid circle) and opposite circularly polarized (red solid circle) pump/probe circular polarization configurations; At the bottom, the spin precession kinetics (blue solid circle) at 484 nm are extracted by subtracting the above two curves. The hollow circle represents the TA kinetics measured at 0 T. The solid black line is the fit.

The research group first studied the injection of hole spin and its precession behavior with the tipping pulse turned off and the pump pulse on (Figure 1d). Circularly polarized pump light triggers electron transfer on a subpicosecond scale, leaving a spin-polarized hole. As shown in Figure 2a, under the applied transverse magnetic field, the hole is in the coherent superposition of the two states of |↑> and |>↓ under the definition of the external magnetic field: (|↑> ± |↓>)/√2, and this coherent superposition is located on the x-axis of the Bloch sphere (whose z-axis is parallel to the magnetic field direction Bz). Since there is a Zeeman split (Ez) between |↑> and |↓>, its coherent state will be in the equatorial plane of the Bloch sphere at an angular frequency ω = Ez/Precession. This precession behavior can be observed by circularly polarized absorption spectroscopy. As shown in the left and right figures of Figure 2c, the oscillation dynamics of the opposite phase can be observed using the pump/detection transient absorption spectral configuration of the same circular polarization and opposite circular polarization at the external magnetic field Bz=0.65 T. From the dynamics of the zero external magnetic field (Bz=0 T), it can be seen that the spin relaxation life is greatly extended compared to QD1 (spin life ~1 ps) without AQ molecular modification (Figure 2d). This shows that electron-hole exchange is indeed the dominant factor limiting exciton spin relaxation in QD at room temperature. In addition, the cosine function S

Ultra-fast handling based on the optical Stark effect

Figure 3: Ultrafast spin manipulation using the optical Stark effect (OSE). (a) Schematic diagram of spin selection OSE for CsPbBr3 quantum dots. Δ is the amount of detuning of the driving photon (σ+) compared to the optical transition energy (Eg); δOSE is OSE-induced optical transition blue shift energy. For simplicity, only the “dress-up” in the Floquet state |-1/2>h is shown, ignoring another state related to “dress-down” in |+1/2>e. (b) Two-dimensional false-color TA spectra of QD1-AQ with (left) identical circularly polarized (σ+/σ+) and (right) opposite circularly polarized (σ-/σ+) tipping pulse/detection configuration. (c) OSE spectrum at zero moment, different tipping power densities. (d) Plotting of OSE displacement (δOSE) as a function of tipping power density (blue circle). The solid gray line is a linear fitted line. (e) Schematic diagram of a Bloch sphere coherently manipulating (left) exciton states and (right) hole states by an effective magnetic field induced by OSE (Beff) along the x-axis (tipping light). Assuming that the electron and the hole bisect the δOSE of the exciton, the hole rotation angle is half of the exciton rotation angle.

The research group studied the OSE effect with tipping light on and pump light off (Figure 1d), when the tested sample is electrically neutral rather than in the hole state. However, this provides a good starting point for the next research. As shown in Figure 3a, under the quasiparticle image, when σ+ tipping light is used to drive the system coherently, its Floquet state is only |-1/2>h state and | +1/2>e state hybridization, with two other states (|-1/2>e state and | +1/2 >h state) does not hybridize. Therefore, σ+ detection light will detect the optical transition of blue shift, while σ-detection light will not.

As shown in Figure 3b, the research team did observe a derivative spectral image with the same circularly polarized tipping-probe. The signal only appears when the tipping pulse and probe pulse coincide. This is in line with the expected circularly polarized transition rule. The derivative spectral signal intensifies linearly with tipping pulse power density Ptip (Figure 3c), which characterizes the energy cleavage (δOSE) of |σ+ > excitons and |σ-> excitons caused by OSE effects. Cleaving increases almost linearly with Ptip and reaches 9.65 meV at 9.72 GW/cm-2. From the slope, it can be deduced that the transition dipole moments of QD1 and QD2 are 21 D and 24 D, respectively. The large transition dipole moment means that the light of CsPbBr3 QDs interacts very strongly with matter. This differs from previously studied CdSe quantum dots, which rely on surface plasmon resonance effects to achieve a similar δOSE.

The strong light-matter interaction in CsPbBr3 QDs favors spin manipulation using the OSE effect. The OSE effect can be understood as an effective pseudomagnetic field (Beff) that demerges decentralised |σ+> excitons and |σ-> excitons. Beff’s direction is along the Tipping (x-axis, Figure 3e left). If one is preparedexciton coherent superposition (|σ+> + |σ->)/√2, which can be rotated by up to ~275° (4.8 radians) around the Beff axis under current conditions. If it is assumed that electrons contribute the same to the hole to δOSE, the hole state will be able to rotate 137.5° (2.4 radians, Figure 3e right).

Room temperature hole spin coherent manipulation

Figure 4: Room temperature hole spin manipulation of CsPbBr3 quantum dots. (a) Spin precession dynamics (gray circle) and tipping dynamics (colored circle) without tipping when the tipping pulse acts on different time delays (where the black arrow is pointing) (top: 17.2 ps; Medium: 31.7 ps; Bottom: 42.0 ps) comparison chart. The solid line is the fitted line. (b) Schematic diagram of a Bloch sphere for coherent hole spin manipulation using a Beff tipping pulse. (c) Spin precession dynamics change plot with tipping power density, tipping time fixed at 17.2 ps (color dot). The solid lines are their fits. (d) Tipping angle of QD1 (blue circle) and QD2 (red triangle) as a function of tipping power density. The solid gray line is the fitted line.

With the spin precession and OSE spin manipulation methods, the research group carried out the manipulation of the hole spin of the QD-AQ system at room temperature under the pump light chopping and tipping light without chopping, and under the applied transverse magnetic field. Firstly, the influence of tipping light on hole spin when it is at different positions on the Bloch sphere is studied. Figure 4a The above figure shows the hole spin dynamics when the time delay ttip=17.2 ps and the Tip power is Ptip=9.72 GW/cm2, when the spin vector is in the Y-axis direction of the Bloch sphere, that is, in the (|↑>+i|↓>)/√2 state. Compared to untipping light, the amplitude of the dynamics of tipping light applied is reduced and the sign changes, and the change of spin vector on Bloch spheres is shown in Figure 4b. However, at ttip=31.7 ps and the same Tip power, there is only a negligible amplitude change (Figure 4a), where the spin vector is in the x-axis direction of the Bloch sphere, i.e., (|↑>-|↓>)/√2 state. The y-axis and x-axis Tip show the most efficient and least effective spin manipulation, and Figure 4a also shows the tip in the general position.

The study group fixed the time delay at ttip=17.2 ps and changed the Ptip (Figure 4c). Fitting the kinetics by the damping oscillation function, θtip=arccos(At⁄Au) can be obtained, where At and Au are the amplitudes with Tip light and without Tip light, respectively. As shown in Figure 4d, the θtip of QD1-AQ increases sublinearly with Ptip (θtip∝PTip0.636) and reaches 2π⁄3 radians at ~10 GW/cm2. The maximum value of θtip is limited by the laser power used. The research team expects that the rotation of π radians can be achieved by changing the width of the Tip, the energy of photons, and the power.

The trend of θtip growing sublinearly with Ptip seems to contradict the linear growth of δOSE with Ptip, but in fact, this situation is similar to the previous situation in the study of epitaxial growth quantum dots. When the interaction between the electric field of Tipping light and the transition dipole moment of QD (i.e., the rabbi energy) can be compared to the amount of detuning (△), the adiabatic elimination approximation is broken, and the research group must consider the virtual state of the cloth. For example, at Ptip=9.72 GW/cm2, QD1 has a rabbian energy of 67.3 meV, which is indeed close to its △≈230 meV. In the references, θtip∝PTip0.65 is calculated based on the four-level principal equation, which is in good agreement with the results obtained here.

Summary and outlook

The researchers achieved the injection, manipulation and readout of hole spin of CsPbBr3 perovskite quantum dots at room temperature, demonstrating the possibility of using low-cost, solution-grown samples for quantum information science at room temperature. In order to be able to complete the spin operation of 104-105 using femtosecond pulses before spinning decoherence, the next step is to extend the spin coherence lifetime to the nanosecond level. (Source: Science Network)

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