Spin Noise Spectroscopy in a Single Quantum Dot at 1550 NM

The method of spin noise spectroscopy allows for optical measurements of spin dynamics in semiconductor nanostructures. Indium gallium arsenide quantum dots are a promising nanostructure that can be integrated into future quantum computing, communication, and cryptography devices. Shifting the emission wavelength of holes inside quantum dots from typically 700 - 900 nm to 1550 nm, the telecom C-band is reached which is prevalent in fibre and communication technologies.

In the history of computers, the size of transistors and other elements of integrated circuits decreases resulting in a rapidly increasing velocity of computations.

As the electronic elements reach the physical and technical boundary of diminution and acceleration, new materials are considered to replace electronics. Quantum dots are one of several approaches to design a new generation of computers that are named quantum computers and work with quantum bits (qubits) instead of electronic bits. Qubits can also be made of a two-level state of single atoms which are volatile and difficult to trap in a fixed spatial position.

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Therefore, nanostructures such as quantum dots that are embedded in solid state systems are considered as a qubit candidate. As the most important advantage over single atoms, these nanostructures can be integrated into laser diodes, cavities and other technical devices. They also fulfil the key requirements for a qubit which are optical implementation, manipulation and read-out (DiVincenzo 2000). Other advantages in comparison with single atoms are the increased photon yield because of a higher oscillator strength and that the wavelength of photon absorption and emittance of the quantum dots (QDs) can be designed by the size of the QD.

Although consisting of typically 106 atoms, a quantum dot shares important optical properties with a single atom and is thus called artificial atom.

Both exhibit resolution-limited linewidths (mean value for QDs: 59 meV), low fine structure splittings, and a discrete spectrum. Moreover, their emission shows photon antibunching in intensity correlation measurements so they can be used as single photon sources in quantum communication technology as well. In quantum cryptography schemes, the essentials are deterministic emission characteristics in generating single photons, entangled photon pairs, and indistinguishable photons (Paul et al. 2017, Michler et al. 2000, Zwiller et al. 2001), Rabi oscillation, and Mollow triplet (Kamada et al. 2001, Xu and Berman 2007). On the other hand, QDs have also disadvantages compared to single atoms, such as a shorter decoherence time caused by the solid state environment. This results in interaction and noise. For the application of QDs in quantum computers, the coherence time describes the duration of maintaining information inside a qubit. So it is important to understand the mechanisms that lead to noise, e.g. fluctuations of the charge distribution near the position of the QD (Kuhlmann et al. 2013), Auger recombination and other non-radiative decay processes which result in a decrease of the photon yield (Crooker et al. 2004).

Due to the high amount of nuclear spins in a single QD causing a fast electron spin decoherence within a few nanoseconds, the hyperfine interaction is the dominant noise mechanism at low temperatures which are applied in spin noise spectroscopy experiments. This effect can be mitigated by using hole spins instead of electron spins. The typical band structure of bulk indium arsenide (InAs) is depicted in Figure 1. As a consequence of the p-type Bloch function of the holes in the valence band in contrast to the s-type Bloch function of the electrons in the conduction band, the interaction between holes and nuclei is weaker so the spin lifetime is increased (Brunner et al. 2009, Eble et al. 2009). Thus, the spin dynamics are important for the coherence time in QDs.

The spin coherence can be also elongated by an external magnetic field. The optical properties of holes are also caused by the band structure. Because of the conservation of energy and momentum, optical selection rules allow only certain transition for both absorption and emission of photons. An excited electron leaves a hole in the valence band behind thus forming an electron-hole complex called exciton. A common material for QDs is a heterostructure consisting of indium arsenide (InAs) QDs embedded in a matrix of GaAs. The indium can be deposited on the GaAs substrate by metal-organic vapor-phase epitaxy. For the fabrication of QDs for experiments with light-matter interaction, self-assembly is a beneficial process. Due to the mismatch of the lattice constants of 7%, the strain enables islands to form after the growth of about 1.7 monolayers. As a consequence, a three dimensional trapping potential is built inside these islands for charge carriers with a spin.

This confinement is the reason for the quantized energy levels for carriers, for the discrete photon energy levels, for the bright transitions as well as for the optically driven, coherent and strong interaction between light and matter (proven by Rabi oscillation and Mollow triplet (Kamada et al. 2001, Xu and Berman 2007)). In order to obtain optimal optical properties, the growth conditions and the amount of deposited indium have to be controlled during the growth process to minimize the amount of crystal defects (Gywat et al. 2010, Tartakovskii 2012).

By producing structures with low area densities of QDs, single quantum dots can be addressed. Figure 1: Typical size (a) and valance band structure (b) of a quantum dot that is grown in self-assembly inside a semiconductor heterostructure including heavyhole (hh), light-hole (lh) and split off (so) subbands. Due to the energy splittings of the subbands, the s-shell of the QD can be devided into four states: mz = ±1/2 for electrons in the conduction band and mz =±3/2 for holes in the valence band (Wiegand 2019). Typical wavelengths of photon absorption and emittance of QDs range from 800 to 900 nm. Higher wavelengths in the telecom O-band at 1310 nm and C-band at 1550 nm are desirable for the integration into fibre based technologies and for long-distance free space applications based on the glass fibre and atmosphere transmission windows. This shift of the spectrum can be achieved by reducing the stress in the QDs. Therefore, the residual strain at the surface of the metamorphic buffer layer is decreased. Consequently, the lattice mismatch between the QD material and the growth surface is reduced to about 4.8 % (Semenova et al. 2008, Paul et al. 2017.) An earlier approach to increase the wavelength was covering the QDs with a strain reducing layer made of InGaAs but this cannot reach the telecom C-band. Olbrich et al. 2017 succeeded for the first time in building a single photon source with QDs emitting photons at 1550 nm.

Traditionally, pump-probe measurements are used to observe the spin dynamics. As this requires optical pumping which leads to hot carriers and impedes the measurement in thermal equilibrium. Therefore, a new method of spin noise spectroscopy (SNS) has been recently developed to map the fluctuations of the spin in the ground state using Faraday rotation of linear polarized light of a probe laser. First, the spin dynamics of atomic gases were measured with SNS by Kurzmann et al. 2016, Aleksandrov and Zapasskii 1981. Later SNS was transferred to bulk electron spins in gallium arsenide (GaAs) by Oestreich et al. 2005. Crooker et al. 2010 published the first spin noise spectroscopy experiment on quantum dots focusing on measurements of the gyromagnetic factor. On the one hand, the fast spin relaxation of holes has impeded the observation of spin dynamics of holes in bulk semiconductors and quantum wells. On the other hand, the spin polarization of holes in quantum dots at the 𝛤 point (k = 0) can exceed the typical value of 50% in bulk GaAs (Müller 2010).

Hole spin dynamics were measured by SNS by Dahbashi 2011. As SNS does not require spin-polarized carriers but extracts the intrinsic spin dynamics from the measurement of the spin noise, the SNS mitigates disturbing the spin dynamics and spin relaxations due to optical excitation (Zapasskii 2013, Römer et al. 2007). This is the main advantage of SNS over pump-probe experiments. To handle the SNS theoretically, the fluctuation-dissipation theorem explains the noise spectrum as the combination of the thermal equilibrium state with the linear response function to an external perturbation (Kubo 1966, Sinitsyn and Pershin 2016). In the case of strong external perturbation this is not valid, e.g. optical interrogation and manipulation.

The principle of SNS is depicted in Figure 2. The linear polarization of the probe laser light is rotated by the Faraday effect. This rotation angle fluctuates depending on the spin noise. By a spectral analysis of the average noise signal, the spin dynamics of the ground state of the QD can be measured. Figure 2: Spin noise spectroscopy experiments use linear polarized light from a probe laser that is rotated by the Faraday effect depending on the thermal fluctuations of the spin in the QD ground state (figure from Wiegand 2019). Spin noise spectroscopy is a promising new method for measurements of the spin dynamics in semiconductor nanostructures to evaluate the possibility of integrating quantum dots into quantum computing, communicating and cryptography devices. By using quantum dots at the telecom C-band as qubit candidates, they can be combined with the prevalent fibre and communication technologies can be combined in the future.