## Scope of research

Electron and hole spins in solid-state nano-structures possess unique properties with favourably long spin coherence, and with high potential for fast coherent optical, magnetic and electrical control. The major challenge we undertake in our studies on this subject is the realisation of spin-qubits based on single spins with coherence in the ms range, and the development of optical and microwave control strategies enabling fast hole and electron spin operations in single quantum dots (QDs). In III-V semiconductor nano-structures the dominant mechanism of spin information leakage to the environment (decoherence) is magnetic interaction with slowly fluctuating nuclear spins of the lattice. In our experiments we have learned a great deal about nuclear spins, and have developed new nuclear magnetic resonance (NMR) techniques for control of tiny ensembles of nuclear spins in semiconductor QDs. These studies have opened new possibilities for non-invasive structural studies using nano-NMR, and in future will allow exploration of unusual collective behaviour of nuclear spins in nano-structures.

## Experimental laboratories

Our main experimental technique is photoluminescence spectroscopy of individual semiconductor quantum dots at low temperatures and high magnetic fields. In our laboratories we have three liquid-helium bath cryostats equipped with superconducting magnets (including one vector magnet system). To detect photoluminescence we use high-resolution single and double spectrometers coupled to state of the art low-noise, liquid-nitrogen-cooled CCD cameras (detection efficiency up to 90%). Top-range radiofrequency and microwave equipment is used for NMR and microwave-spin-control projects respectively.

## Contact details

For any inquiries please contact Dr. Evgeny Chekhovich

## Research highlights

**Prototype two-qubit quantum processor running on nuclear spins of a quantum dot**

Over the past two decades nuclear spins were largely viewed as an unsolvable problem of the III-V semiconductor quantum dots. Here we show that the spin-3/2 quadrupolar nuclei of a dot can be engineered into a “clean” nanoscale quantum system. We demonstrate experimentally the entire toolkit of quantum information processing, including implementation of benchmark quantum computing algorithms.

**Emergent quantum thermodynamic behavior in a system of interacting nuclear spins**

Preserving quantum coherence over long timescales is a key requirement for quantum information processing applications. Here we develop pulse control sequences for dynamical preservation of the coherence and test them on a nuclear spin bath of a quantum dot. We discover the distinct regimes of decoherence depending on the type of the spin bath: for homogeneous spin baths the coherence storage time can be extended by orders of magnitude, whereas for inhomogeneous (strongly disordered) spin baths the coherence is found to be fundamentally limited by the irreversible conversion of coherence into many-body spin-spin quantum entanglement. The effect is similar to the second law of thermodynamics, where useful energy is irreversibly converted into wasteful heat, demonstrating emergence of thermodynamic effects in a nanoscale system.

**Nuclear spin effects in CdTe/ZnTe quantum dots**

The II-VI semiconductors offer a unique combination of attractive properties: direct-bandgap character offers a good interface between electron spin qubits and photons, while most nuclei are spin-free, suppressing the source of spin qubit decoherence that plagues the III-V semiconductors. Previous studies of nuclear spins in II-VI quantum dots relied on indirect detection, leaving beyond reach the most interesting regime of strong magnetic fields (>0.1 T). Here we achieve direct detection of the hyperne shifts in individual CdTe dots and demonstrate fast optical initialization, long persistence and radio-frequency manipulation of the nuclear spin magnetization. Our studies confirm II-VI dots as a promising platform for hybrid electron-nuclear spin qubit registers, not achievable in III-V materials.

**Nuclear spin thermometry in quantum dots**

Previous measurements of the state of a quantum dot nuclear spin bath were limited to mean-field approaches, which lack accuracy due to the spatial inhomogeneity of the nuclear polarization and uncertainty in hyperfine constants. We have developed an alternative NMR-based approach where the state of the nuclear spin ensemble is probed directly by measuring its spin temperature. Our studies lead to observation of record-high nuclear spin polarization in a quantum dot (~80%), revealed the non-equilibrium nature of the optically-cooled nuclei, and allowed the hyperfine constants of GaAs to be measured for the first time.

**Probing nuclear spin bath fluctuations in strained quantum dots**

One of the key challenges in spectroscopy is the inhomogeneous broadening that masks the homogeneous spectral lineshape. In strained self-assembled quantum dots inhomogeneous broadening of the nuclear spin ensemble is so large, that the standard spin-echo techniques using high power radio-frequency (rf) pulses no longer work. We have developed new NMR techniques that rely on low-power non-coherent rf pulses whose spectral profiles resemble a comb. This frequency comb NMR method not only gives measure of the hidden homogeneous NMR lineshapes, but also reveals the few-second-long correlation times of the subtle nuclear spin fluctuation dynamics, which can not be detected with standard NMR methods.

**Coherent NMR spectroscopy on self-assembled quantum dots**

Using high-sensitivity optical detection we demonstrated for the first time coherent NMR spectroscopy on few thousand nuclear spins in individual self-assembled quantum dots. Large quadrupolar effects arising from the lattice mismatch, driving the quantum dot self-assembly, were found to increase significantly the nuclear spin coherence times T_{2}. Such increase in T_{2} is a clear sign of the strain-induced suppression of the nuclear spin fluctuations, which opens the way for achieving long electron and hole spin coherence in self-assembled quantum dots.

**Hole hyperfine interaction in quantum dots**

Using photoluminescence spectroscopy of both “bright” and “dark” (optically forbidden) excitons we were able to measure the interaction of the valence band holes with nuclear spins. Furthermore, using NMR techniques we found a way to probe hole hyperfine interaction constants individually for each isotope. To our surprise we found that cations and anions have opposite signs of the hyperfine constants. This can only be explained if we take into account significant contribution of the *d*-symmetry atomic orbitals into the valence band states, which were previously thought to be constructed of *p*-orbitals only.

**Structural analysis of strained quantum dots using NMR**

Nuclear magnetic resonance (NMR) is a powerful analysis tool used in chemistry, biology and material science studies. However, application of NMR to strained nanostructures, such as self-assembled quantum dots, has been problematic due to huge strain-induced broadening of the NMR spectra. We have developed a special “inverse” NMR technique, which effectively solved this problem and allowed us for the first time to probe chemical composition and distribution of strain within a few-nanometer volume of an individual quantum dot.