## AMOP SEMINARS

#### Usually held on Mondays at 3.30pm in the Ryle seminar room 930

**04.03.19 Prof. Jeremy Baumberg **

* NanoPhotonics Centre, Cavendish Laboratory, University of Cambridge*

### Spin-Josephson coupling and the phase diagram of polariton condensate arrays

Polaritons are light-matter quasiparticles which exist within wavelength-scale microcavities that couple confined photons with semiconductor excitons. Over the last decades these bosons have been found to exhibit nonequilibrium Bose-Einstein condensation, with interaction energies sufficient to give room temperature condensates. Here we will show how advances now allow arrays of interacting condensates to be explored, and show the crucial role of magnetization in some situations. We show the unusual spontaneous symmetry breaking for the magnetisation of a polariton condensate.[1,2] Unpolarised incoherent pumping generates randomly spin-up or spin-down magnetised condensates on each realisation, which remain stable for seconds, but can be rapidly switched sub-ns. By applying an electrical field perpendicular to the quantum-well plane we precisely tune the polarisation of the condensate emission. We utilise this to realise an electrical spin-switch, operating at record ultra-low switching energies of the order of attojoules and switching speeds that are only limited by the condensate dynamics (hundreds of picosecond).[3] The direction of the spin of two neighbouring condensates can also be controllably aligned (ferromagnetic) or anti-aligned (antiferromagnetic) by optically tuning their coupling strength. Building on this, we recently realized an optically controlled lattice of spin-polarized polariton condensates where we observe ferromagnetic and antiferromagnetic phases, and at the crossover between these two phases an unusual paired-spin phase.[4] We also observe new array interactions of condensates, showing how coherence evolves across the entire array. These properties, which are due to the non-equilibrium and non-linear nature of polariton condensates, give strong hopes for a whole variety of optoelectronic devices as well as outlining a completely new route towards utilising non-linear non-equilibrium coupled polariton condensates for complex simulations.

[1]Phys. Rev. X 5, 031002 (2015), H Ohadi et al, Spontaneous spin bifurcations and ferromagnetic phase transitions in a spinor exciton-polariton condensate

[2]PRL 116, 106403 (2016), H Ohadi et al, Tunable Magnetic Alignment between Trapped Exciton-Polariton Condensates

[3]Nature Mat. 15, 1074 (2016), A. Dreismann et al, A sub-femtojoule electrical spin-switch based on optically trapped polariton condensates

[4]PRL 119, 067401 (2017), H Ohadi et al, Spin Order and Phase Transitions in Chains of Polariton Condensates

**26.01.19 Dr Claire Le Gall and Dr Dorian Gangloff *Rutherford Seminar Room***

*University of Cambridge*

### Titile tbc

Abstract tbc

**21.01.19 Dr Daniel Oi**

*University of Strathclyde*

### Nanosatellites for Quantum Science and Profit

We are at the start of a quantum space race with pioneering results in bringing quantum physics to space recently achieved. China's Quantum Experiments at Space Scale (QUESS) satellite, also known as Micius, successfully performed entanglement distribution, quantum teleportation, and quantum cryptography to and from orbit. The MAIUS 1 mission produced the first Bose-Einstein Condensate (BEC) in space opening up new possibilities for next generation space quantum clocks and cold atom science. These proof-of-principle demonstrations show the potential for advances in timing, navigation, remote sensing, fundamental science, as well as building the infrastructure for a global quantum internet. In this talk, I will give an overview of the efforts to bring quantum science and technology into space. In particular, I will discuss how CubeSats, kg-class spacecraft, may play a role in this rapidly developing movement.

**27.11.18 Guillaume Salomon *Tuesday 27/11, 2pm Ryle Seminar room***

*Max-Planck-Institut fur Quantenoptik (MPQ), Garching, Germany*

### Quantum gas microscopy of the doped Fermi-Hubbard model

Strongly correlated electronic systems, usually described by the Fermi-Hubbard model, can host a large variety of exotic phenomena such as high-Tc superconductivity and non Fermi liquid behaviour. Our understanding of the doped Fermi-Hubbard model, however, vastly depends on the dimensionality. Whereas powerful analytical and numerical techniques exist in one dimension, its phase diagram is still debated in two dimensions. I report here on our recent experimental studies of this model in both one and two dimensions using spin and density resolved quantum gas microscopy. In 1d, I will describe our direct observation of two fundamental predictions for Luttinger liquids. I will show that incommensurate spin correlations emerge in both doped and spin imbalanced systems and I will provide a microscopic picture for these phenomena. In the particle-doped two-dimensional Fermi-Hubbard model, I will demonstrate that the competition between kinetic and magnetic energy leads instead to the formation of a magnetic polaron. The study of the spin environment around a mobile doublon directly reveals its local dressing by a cloud with reduced antiferromagnetic correlations. In contrast, when pinning a doublon to one lattice site, we observe an opposite effect with increased antiferromagnetic correlations in its vicinity. These works open fascinating perspectives to study strongly correlated quantum many-body systems with single particle and single spin resolution.

**26.11.18 Dr Jinyi Zhang **

*Cavendish Laboratory, University of Cambridge*

### Recent results in 87Rb box trap

Collective excitation or quasiparticle is the key feature of many-body quantum systems. In spite of the rapid progresses in the field of the collective excitation and its damping in ultracold atom system, most of the trapping potentials studied up to now are based on harmonic trap. In this talk, I introduce a new nonlinear damping mechanism in the lowest-lying excitation, based on continually shaking quantum gases in a uniform box trap. We observe power-scaling for damping rate, and propose a minimal model to elucidate the nonlinear damping behaviour.

**and**

**26.11.18 Dr Matteo Brunelli **

*Cavendish Laboratory, University of Cambridge*

### Linear-and-quadratic reservoir engineering of non-Gaussian states in cavity optomechanics

Reservoir engineering is a powerful tool that enables the robust preparation of pure quantum states in noisy environments. It has been successfully employed for the stabilization of squeezed and entangled states in trapped atoms and ions, circuit quantum electrodynamics and optomechanics. However, despite the success, bosonic reservoir engineering is currently limited by the linear character of the evolution, which restricts the set of target states to Gaussian ones. I will discuss a novel scheme for the unconditional preparation of pure non-Gaussian states of a target system. The target mode is nonlinearly coupled to an auxiliary damped mode, which acts as an engineered reservoir. For concreteness, I will discuss an optomechanical realization, where mechanical target states are stabilized in an optomechanical cavity that is parametrically coupled to both the mechanical displacement and the displacement squared. I will show how interesting families of non-Gaussian states, such as the cubic phase state or (squeezed and displaced) finite superpositions of Fock states, can be prepared following this recipe.

**Rescheduled for Lent term -- Prof. Jeremy Baumberg **

* NanoPhotonics Centre, Cavendish Laboratory, University of Cambridge*

### Spin-Josephson coupling and the phase diagram of polariton condensate arrays

Polaritons are light-matter quasiparticles which exist within wavelength-scale microcavities that couple confined photons with semiconductor excitons. Over the last decades these bosons have been found to exhibit nonequilibrium Bose-Einstein condensation, with interaction energies sufficient to give room temperature condensates. Here we will show how advances now allow arrays of interacting condensates to be explored, and show the crucial role of magnetization in some situations. We show the unusual spontaneous symmetry breaking for the magnetisation of a polariton condensate.[1,2] Unpolarised incoherent pumping generates randomly spin-up or spin-down magnetised condensates on each realisation, which remain stable for seconds, but can be rapidly switched sub-ns. By applying an electrical field perpendicular to the quantum-well plane we precisely tune the polarisation of the condensate emission. We utilise this to realise an electrical spin-switch, operating at record ultra-low switching energies of the order of attojoules and switching speeds that are only limited by the condensate dynamics (hundreds of picosecond).[3] The direction of the spin of two neighbouring condensates can also be controllably aligned (ferromagnetic) or anti-aligned (antiferromagnetic) by optically tuning their coupling strength. Building on this, we recently realized an optically controlled lattice of spin-polarized polariton condensates where we observe ferromagnetic and antiferromagnetic phases, and at the crossover between these two phases an unusual paired-spin phase.[4] We also observe new array interactions of condensates, showing how coherence evolves across the entire array. These properties, which are due to the non-equilibrium and non-linear nature of polariton condensates, give strong hopes for a whole variety of optoelectronic devices as well as outlining a completely new route towards utilising non-linear non-equilibrium coupled polariton condensates for complex simulations.

[1]Phys. Rev. X 5, 031002 (2015), H Ohadi et al, Spontaneous spin bifurcations and ferromagnetic phase transitions in a spinor exciton-polariton condensate

[2]PRL 116, 106403 (2016), H Ohadi et al, Tunable Magnetic Alignment between Trapped Exciton-Polariton Condensates

[3]Nature Mat. 15, 1074 (2016), A. Dreismann et al, A sub-femtojoule electrical spin-switch based on optically trapped polariton condensates

[4]PRL 119, 067401 (2017), H Ohadi et al, Spin Order and Phase Transitions in Chains of Polariton Condensates

**01.11.18 Shankari Rajagopal **Thursday, 1/11, 10:00am, Ryle Seminar room****

*University of California, Santa Barbara*

### New Phenomena in Driven Quantum Systems

The isolated, clean, and tunable nature of ultracold gases make them a natural platform for controlled realization and study of Floquet physics and driven quantum systems. I will present recent results from the Weld group discussing three experiments along these lines. First I will discuss an ultracold strontium experiment in which weak driving of a bichromatic lattice is used to probe novel excitation spectra in quasiperiodic systems. I will then talk about ultracold lithium in strongly modulated optical lattices, including the mapping of a Floquet phase diagram and exploration of a Floquet prethermal state. Finally, I will present results from a new type of quantum simulator in which a driven Bose condensate of strontium emulates ultrafast ionization dynamics in attosecond laser pulses, counter-intuitively enabling the study of some of the fastest processes in atomic physics with some of the slowest.

**08.10.18 Dr. Lucia Hackermüller **

*University of Nottingham*

### Experiments with ultracold Li and cold Cs atoms

We present results of our three experimental setups. For our molecular lithium BEC we study strongly interacting systems insitu and compare the profile and temperature to a semi-ideal description and to a full Hatree-Fock description. In addition we explore non-equilibrium effects in the Li-Li molecule creation. We also have built an atom-photon interface, by trapping cold Cs atoms in an intersection of an optical fibre. For this we laser drill a 30 µm through-hole orthogonal to the fibre and trap about 300 atoms in the interaction region. Trapping the atoms in the centre of the guided light mode allows excellent overlap of photons and atoms. In addition we simulate different hole-shapes in order to find optimum transmission. We show that with the addition of a cavity reaching the strong coupling regime should be possible. We will also report on our efforts to build small, compact and portable quantum systems.

**06.09.18 Prof. Monika Schleier-Smith **Thursday, 6/9, 3:30pm, Ryle Seminar room****

*Stanford University*

### Interfacing Spins with Photons for Quantum Simulation and Quantum Control

Coupling many atoms to a single mode of light provides an efficient means of spreading quantum information across an extended many-body system. I will report on experiments in which we harness photons in an optical cavity to mediate “flip-flop” interactions among distant spins in a millimeter-long cloud of atoms. We characterize the spin-exchange interactions via quench dynamics and imaging of the local magnetization, demonstrating optical control of the interactions' strength and sign. Furthermore, we observe signatures of correlated pair creation in Zeeman states of a spin-1 system, a light-mediated analog of collisional spin mixing in Bose-Einstein condensates. In contrast to direct collisional interactions, non-local photon-mediated interactions offer unprecedented opportunities for engineering the spatial structure of spin-spin couplings and correlations. I will describe prospects for tailoring the interactions to enable new directions in quantum simulation and to generate new resources for quantum-enhanced sensing.

**20.8.18 Dr.**** **Davide Bossini

*Technische Universität Dortmund, Germany*

### Ultrafast optical manipulation of magnetic materials

Magnetism in solid state materials is one of the most widely investigated phenomena in condensed matter physics. The conventional description of a magnetic material is formulated in the framework of thermodynamics, since it relies on the concept of equilibrium. While this approach is effective for the ground state properties, its application to the dynamical regime is limited to to spin dynamics with characteristic timescales in which the adiabatic approximation can still be invoked. The technical progresses of pulsed laser sources have provided the possibility to generate intense laser pulses with duration in the 10-100 femtosecond range. Such laser pulses are among the shortest stimuli in contemporary solid state physics. They provide the groundbreaking possibility to drive and detect spin dynamics in magnetic materials in real-time experiments, whose time-resolution is comparable to or even shorter than the two main magnetic interactions, i.e. the spin-orbit coupling and the exchange interaction. Note that aside from the clear academic interest, investigating the optical control of spins on ever-shorter timescales may have relevant implications for possible future developments of the magnetic recording industry. In this talk I will present the basic concepts, methods and goals of the feld called “ultrafast magnetism”[1]. In particular, I aim at demonstrating the potentiality and wide applicability of the optical methods, by describing the major breakthroughs reported in this research area. Spectacular phenomena have already been observed, such as the ultrafast demagnetisation[2], the picosecond-deterministic reversal of the magnetisation[3], the coherent control collective spin excitations[4] and even the photo-induced magnetic phase transitions on the picosecond timescale[5]. In the last part of my talk, I plan to discuss the most recent trends[6,7] and some possible future directions.

[1] A. Kirilyuk et al. Rev. Mod. Phys. 82, 2731 (2010)

[2] E. Beaurepaire et al. PRL 76, 4250 (1996)

[3] C. Stanciu et al. PRL 99, 047601 (2007)

[4] A.V. Kimel et al Nature 435, 655 (2005)

[5] D. Afanasiev et al. PRL 116, 097401 (2016)

[6] D. Bossini et al. Nat. Comm. 7, 10645 (2016)

**04.07.18 ******Wednesday 11am Rutherford Seminar Room B** ****Prof. Martin Zwierlein **

**Massachusetts Institute of Technology, Cambridge MA, USA**

### Quantum transport in strongly interacting Fermi gases

Understanding transport in strongly interacting systems of fermions is one of the outstanding challenges in many-body physics. There exist many open questions even on the qualitative features of such transport, whether it can be described by quasi-particles, whether heat, charge and spin are transported together or separately, and how transport properties change across phase transitions. I will present measurements of sound attenuation in strongly interacting, homogeneous Fermi gases, which reveal quantum limited sound diffusivity even in the superfluid regime. For Fermi gases in the Hubbard regime, observed under a microscope with single-atom resolution, we performed studies of spin transport in the Mott insulating regime, where charge is frozen but spins are free to diffuse. We obtain spin diffusivities revealing super-exchange scaling, with contributions from direct tunnelling of spins facilitated by doublon-hole fluctuations.

**19.06.18 ******Tuesday** ****Prof. Marko Žnidarič **

**University of Ljubljana, Slovenia**

### Interaction instability of localization in quasiperiodic systems

For classical systems with a finite number of degrees of freedom KAM theorem guarantees stability of integrable systems for sufficiently small perturbations. How about quantum systems in the thermodynamic limit?

I will present results showing that systems with quasiperiodic potential can behave completely differently than random ones, where dynamics smoothly changes. Namely, for small interactions there is a discontinuous change from localization to diffusion. Implications for possible many-body localization will be discussed. I will also briefly mention exact results for entanglement dynamics in a putative many-body localized system described by a so-called l-bit Hamiltonian, showing that the growth is not just logarithmic in time as believed so far.

**11.06.18 Dr. Fabrice Gerbier**

**Ecole Normale Supeerieure Paris, France**

### Anomalous momentum diffusion of strongly interacting bosons in optical lattices

Dissipative quantum systems are subject to decoherence, the disappearance of interference phenomena due to irreversible loss of information. This plays a role in many modern areas of research, from research on the foundations of quantum mechanics to quantum information processing (and quantum technologies in general), where decoherence is a threat that must be countered. While decoherence has been extensively studied for simple systems, such as a two-level atom or a harmonic oscillator, much less is known for many-body systems of interacting particles. In this talk, I will report on an experimental study of how spatial coherence in a superfluid gas of bosonic atoms in an optical lattice is lost when the atoms undergo spontaneous emission. For independent atoms excited by a near-resonant laser, repeated laser photon absorption-spontaneous emission cycles destroy spatial coherences on distances larger than the wavelength of the optical transition, or equivalently leads to diffusion in momentum space with a momentum width scaling as t^(1/2). This momentum diffusion process is well-known in quantum optics and limits the temperature achievable in laser cooling. For strongly interacting bosons, we observed that the momentum diffusion is anomalously slow: After a short time, the decay of spatial coherences slows down, and momentum space dynamics becomes sub-diffusive with a momentum width scaling as t^(1/4). We explain this behavior in terms of a model proposed by Poletti et al. [1], where the long-times dynamics is understood in terms of a diffusion in Fock space. Dissipation leads to the formation of "long-lived" clusters of atoms with higher occupancy than the average site. These clusters decay slowly (through high-order processes) due to their energy mismatch with more typical configurations. In classical statistical mechanics, the transport dynamics of systems with a distribution of lifetimes featuring a slow tail typically shows sub-diffusion [2]. Using three-body losses as a probe of on site statistics, we provide a direct evidence of this anomalous diffusion in Fock space which underlies the anomalous momentum diffusion.

[1] D. Poletti et al., Phys. Rev. Lett. 109, 045302 (2012); D. Poletti et al., Phys. Rev. Lett. 111, 195301 (2013).

[2] J.-P. Bouchaud, A. Georges, Physics reports 195 (4-5), 127-29 (1990).

**4.06.18 Dr. Tobias Donner**

**ETH Zurich, Switzerland**

### Cavity-mediated interaction in a quantum gas - From supersolids to spin textures

Merging quantum gases with cavity QED allows to engineer long-range interactions between the atoms. If these interactions are sufficiently strong, phase transitions to self-organized crystalline structures of matter and light can take place. We realize a phase transition from a superfluid gas to a supersolid, where a continuous spatial symmetry is broken. The real-time access to the intra-cavity light fields allows us to directly identify the associated phase and amplitude modes. In a different set of experiments, we exploit the vectorial polarizability of the atoms and observe the formation of a spin texture in a multi-level atomic Bose-Einstein condensate.

**20.3.18 Prof. Sabrina Maniscalco Tuesday, 10:00am, TCM Seminar room, Mott building, 2nd floor**

**University of Turku, Finland**

### Quasiperiodic lattices as tunable quantum reservoirs: exploring the Markovian to non-Markovian crossover

Fermionic systems under the influence of quasiperiodic fields display different relaxation properties. In particular, employing bichromatic optical lattices and initial fermionic gases prepared in the so called charge density wave state, the crossover from ergodic to non-ergodic dynamics can be witnessed monitoring the density imbalance in the occupation of even and odd sites.

We investigate such setup from an open quantum system theory perspective, designing a protocol in which an impurity atom is coupled to the fermionic cloud trapped in the bichromatic lattice. This interaction induces decoherence in the probe induced by the complex out-of equilibrium environment. We focus our attention on the time evolution of the impurity in such environment and study wether the probe dynamics can be classified as Markovian or non-Markovian. Specifically we see how the localised phase of the Aubry-Andre’ model displays evidence of strong memory effects.

**19.03.18 Dr. Bernhard Urbaszek Monday, 3:30pm, RYLE Seminar room**

**CNRS – Toulouse University, France**

### Light-matter interaction in atomically thin semiconductors: darkness, brightness, spins and valleys

Transition metal dichalcogenides (TMDCs) such as MoS2 and WSe2 are layered materials that are semiconductors with a direct bandgap when thinned down to one monolayer. Despite an incredible number of results published in the field since 2010, many basic parameters such as the effective carrier mass are not experimentally determined – which leaves plenty of room for further exploration of these fascinating materials. Even samples exfoliated in ambient conditions with simple scotch-tape methods show remarkable properties for optoelectronics and spintronics: TMDC monolayers strongly interact with light in the visible region of the optical spectrum. The optically generated electrons and holes form excitons with high binding energy (several hundred meV) and high oscillator strength, resulting in optical absorption up to 20 % per monolayer. Interband optical selection rules are polarization selective (chiral). This allows addressing non-equivalent valleys in momentum space with polarized lasers for optical spin and valley index manipulation.

We access the optical and spin properties, studying valley dynamics for different exciton species and resident carriers, with unprecedented detail in TMDC monolayers sandwiched between ultrathin insulating layers of hexagonal boron nitride (hBN) in van der Waals heterostructures. The optical emission of these encapsulated monolayers is spectrally narrow (down to 1 nm FWHM) comparable to emission from III-V quantum well structures used in today’s optoelectronic devices and approaching the homogenous limit. This insight paves the way for integrating TMDCs in photonic devices and ferromagnetic- semiconductor heterostructures.

**16.01.18 Dr. Philipp Preiss **Tuesday, 3:30pm, RUTHERFORD Seminar room****

**Heidelberg University, Germany**

### Quantum Simulation of Mesoscopic Fermi Systems

Ultracold quantum gases in optical potentials have achieved spectacular progress in the experimental simulation of complex quantum systems. Complementary to many-body experiments, mesoscopic systems comprised of a small number of atoms offer the possibility to study entangled quantum states with an exceptional degree of versatility and control.

We have implemented a highly tunable platform to study such correlated few-fermion systems. Using reconfigurable optical microtraps, we prepare quantum states of 6Li atoms with a deterministic atom number and spin configuration and tune interactions via a magnetic Feshbach resonance. A novel readout scheme with single-particle sensitivity allows us to measure spin-resolved correlation functions in position and in momentum space.

Such correlators characterize few-body systems via the coherence and symmetry of the wavefunction. Focusing on the Fermi-Hubbard double-well, we observe high-contrast interference of indistinguishable fermions, the build-up of correlations due to interactions, and the emergence of entanglement between particles. Our techniques can be applied to larger systems to characterize many-body phases via their higher-order correlation functions.

**16.10.17 Prof. Alain Aspect **

**Institut d'Optique Graduate School Université Paris-Saclay**

### Hanbury Brown-Twiss, Hong-Ou-Mandel, and other landmarks in quantum optics : from photons to atoms

The second quantum revolution is based on entanglement, discovered by Einstein and Schrödinger in 1935. Its extraordinary character has been experimentally demonstrated by landmark experiments in quantum optics.

At Institut d'Optique, we are currently revisiting these landmarks using atoms instead of photons, and after the observation of the atomic HOM effect^{1}, we are progressing towards a test of Bell's inequalities with pairs of momentum entangled atoms^{2}.

1. Lopes, R., Imanaliev, A., Aspect, A., Cheneau, M., Boiron, D., & Westbrook, C. I. (2015). Atomic Hong-Ou-Mandel experiment. *Nature*, *520*(7545), 66-68.

2. Pierre Dussarrat, Maxime Perrier, Almazbek Imanaliev, Raphael Lopes, Alain Aspect, Marc Cheneau, Denis Boiron, and Christoph I. Westbrook: A two-particle, four-mode interferometer for atoms, arXiv 1707. 01279, to appear in Phys. Rev. Lett..

**30.10.17 Dr. Eva-Maria Graefe **

**Mathematical Physics Group, Faculty of Natural Sciences, Imperial College London**

### Evolution of Gaussian wave packets in the presence of losses and gains

In recent years there has been growing interest in open quantum systems described by non-Hermitian Hamiltonians in various fields. Examples are scattering systems and the effective description of absorption and amplification. The classical counterparts of non-Hermitian quantum systems, however, remained illusive. In this talk I present results on the quantum evolution of Gaussian wave packets generated by a non-Hermitian Hamiltonian in the semiclassical limit of small hbar. This yields a generalisation of the Ehrenfest theorem for the dynamics of observable expectation values. The resulting equations of motion for dynamical variables are coupled to an equation of motion for the phase-space metric - a phenomenon having no analogue in Hermitian theories. The insight that can be gained by this classical description will be demonstrated for a number of example systems.

**13.11.17 Internal Double Feature **

*AMOP, Cavendish*

### Ultracold Bose soup: where few-body meets many-body physics

#### Loss, correlation and energy dynamics of a Bose gas quenched to unitarity

### Daniel Malz (Nunnenkamp group)

#### Nonreciprocity through reservoir engineering in cavity optomechanics

**27.11.17 Prof. Eric Cornell 11**

**JILA, University of Colorado, Boulder, CO, USA**

**Ultracold Bose soup: where few-body meets many-body physics**

**Ultracold Bose soup: where few-body meets many-body physics**

Degenerate bose gases were first created in labs about twenty years ago. These gases now come in many varieties and their microscopic properties may be probed with a diverse range of experimental tools. Degenerate bose *liquid*, on the other hand, is available in any element the customer wants, but only if that element is helium, and even a century after it was first realized, microscopic experimental probes are relatively limited. Can we make our ultracold bose gases more liquid-like? On the way, can we learn some interesting things at the interface between few- and many-body physics?

**11.12.17 Internal Double Feature **

*AMOP, Cavendish*

### Dorian Gangloff (Atature group)

#### Controlling mesoscopic nuclear spin ensembles

### Ed Carter (Schneider group)

#### Quantum Walks in four dimensions

Davide Bossini

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