Coherent superposition states of a mesoscopic quantum object play a major role in our understanding of the quantum to classical boundary, as well as in quantum-enhanced metrology and computing. However, their practical realization and manipulation remains challenging, requiring a high degree of control of the system and its coupling to the environment. Here, we use dysprosium atoms-the most magnetic element in its ground state-to realize coherent superpositions between electronic spin states of opposite orientation, with a mesoscopic spin size J = 8. We drive coherent spin states to quantum superpositions using non-linear light-spin interactions, observing a series of collapses and revivals of quantum coherence. These states feature highly non-classical behavior, with a sensitivity to magnetic fields enhanced by a factor 13.9(1.1) compared to coherent spin states-close to the Heisenberg limit 2J = 16-and an intrinsic fragility to environmental noise.
Coherent superposition states of a mesoscopic quantum object play a major role in our understanding of the quantum to classical boundary, as well as in quantum-enhanced metrology and computing. However, their practical realization and manipulation remains challenging, requiring a high degree of control of the system and its coupling to the environment. Here, we use dysprosium atoms-the most magnetic element in its ground state-to realize coherent superpositions between electronic spin states of opposite orientation, with a mesoscopic spin size J = 8. We drive coherent spin states to quantum superpositions using non-linear light-spin interactions, observing a series of collapses and revivals of quantum coherence. These states feature highly non-classical behavior, with a sensitivity to magnetic fields enhanced by a factor 13.9(1.1) compared to coherent spin states-close to the Heisenberg limit 2J = 16-and an intrinsic fragility to environmental noise.
The precision of a quantum sensor can overcome its classical counterpart when its constituents are entangled. In Gaussian squeezed states, quantum correlations lead to a reduction of the quantum projection noise below the shot noise limit. However, the most sensitive states involve complex non-Gaussian quantum fluctuations, making the required measurement protocol challenging. Here we measure the sensitivity of nonclassical states of the electronic spin J=8 of dysprosium atoms, created using light-induced nonlinear spin coupling. Magnetic sublevel resolution enables us to reach the optimal sensitivity of non-Gaussian (oversqueezed) states, well above the capability of squeezed states and about half the Heisenberg limit.
The sensitivity of quantum sensors is fundamentally constrained by the standard quantum limit (SQL) arising from intrinsic quantum fluctuations. While non-classical resources like squeezing or entanglement can surpass this limit, their utility is often restricted by the extreme fragility of entangled states and the complexity of their preparation. Quantum criticality offers a compelling alternative by harnessing divergent susceptibility to amplify signals without requiring fragile non-classical resources. However, the practical benefit of this approach has remained controversial due to the potential for the simultaneous amplification of quantum noise. Here, we demonstrate a universal protocol for noiseless critical sensing by engineering a light-driven atomic ensemble near a dynamical critical point. Analogous to a Kapitza pendulum near its inverted orientation, the spin system enters a non-equilibrium regime where the signal susceptibility diverges while the quantum noise periodically recedes to its coherent baseline. We exploit this ``noise ebbing'' to create a built-in noiseless amplifier, demonstrating a 3.3 dB metrological gain over the SQL in an atomic magnetometer. Our implementation exhibits intrinsic robustness against common experimental imperfections such as detection losses, establishing non-equilibrium critical dynamics as a practical and versatile paradigm for surpassing the fundamental limits of quantum sensing.
Quantum metrology is a powerful tool for explorations of fundamental physical phenomena and applications in material science and biochemical analysis. While in principle the sensitivity can be improved by increasing the density of sensing particles, in practice this improvement is severely hindered by interactions between them. Here, using a dense ensemble of interacting electronic spins in diamond, we demonstrate a novel approach to quantum metrology to surpass such limitations. It is based on a new method of robust quantum control, which allows us to simultaneously suppress the undesired effects associated with spin-spin interactions, disorder, and control imperfections, enabling a fivefold enhancement in coherence time compared to state-of-the-art control sequences. Combined with optimal spin state initialization and readout directions, this allows us to achieve an ac magnetic field sensitivity well beyond the previous limit imposed by interactions, opening a new regime of high-sensitivity solid-state ensemble magnetometers.
Quantum spins of mesoscopic size are a well-studied playground for engineering nonclassical states. If the spin represents the collective state of an ensemble of qubits, its nonclassical behavior is linked to entanglement between the qubits. In this paper, we report on an experimental study of entanglement between two subsystems of dysprosium's electronic spin. Its ground state, of angular momentum J=8, can formally be viewed as a set of 2J qubits symmetric upon exchange. To access entanglement properties, we partition the spin by optically coupling it to an excited state ${J}^{\ensuremath{'}}=J\ensuremath{-}1$, which removes a pair of qubits in a state defined by the light polarization. Starting with the well-known W and squeezed states, we extract the concurrence of qubit pairs, which quantifies their nonclassical character. We also directly demonstrate entanglement between the 14- and 2-qubit subsystems via an increase in entropy upon partition. In a complementary set of experiments, we probe decoherence of a state prepared in the excited level ${J}^{\ensuremath{'}}=J+1$ and interpret spontaneous emission as a loss of a qubit pair in a random state. This allows us to contrast the robustness of nonclassical pairwise correlations of the W state with the fragility of the coherence involved in a Schr\"odinger cat state. Our findings open up the possibility to engineer novel types of entangled atomic ensembles, in which entanglement occurs within each atom's electronic spin as well as between different atoms. Qubit ensembles with large entanglement depth could then be realized with a few atoms only, facilitating the scaling up of quantum-enhanced sensors.
This thesis describes three studies using ultracold gases of bosonic dysprosium atoms. We encode quantum states of interest in the large electronic ground state spin J=8 of each atom. Narrow-line optical transitions are used to manipulate these states by creating strong spin-dependent tensor light shifts with negligible heating. Our detection scheme uses arbitrary spin rotations followed by measurement of projection probabilities with single magnetic sublevel resolution. Firstly, we study a transverse-field Ising model of quantum spin-1/2’s with infinite-range interactions. This model shows a paramagnetic to ferromagnetic quantum phase transition in the thermodynamic limit. Our experiment relies on the formal equivalence between the states of a spin J=8 and exchange-symmetric states of 2J=16 qubits in the sector of maximum total spin. We probe the thermodynamic and dynamical properties, revealing finite-size quantum critical behaviour around the transition point. We also directly test the fundamental link between symmetry breaking and the appearance of a finite order parameter. This is enabled by access to the collective observable defining the underlying Z2 symmetry. Secondly, we partition the electronic spin to reveal entanglement in nonclassical states. By optically coupling the ground level to an excited state J' = J-1, we remove a pair of encoded qubits in a state defined by the light polarisation. We probe the concurrence of qubit pairs extracted from W and squeezed states to quantify their nonclassical character. We directly demonstrate entanglement between the 14- and 2-qubit subsystems via an increase in entropy upon partition. In a complementary set of experiments, we probe the decoherence of a state prepared in the excited level J' = J + 1 and interpret spontaneous emission as a loss of a qubit pair in a random state. This allows us to contrast the robustness of nonclassical pairwise correlations of the W state with the fragility of the coherence of a Schrödinger cat state. Thirdly, we simulate a quantum Hall system by exploiting the electronic ground state spin as a discrete synthetic dimension, and optically coupling it to atomic motion along a second real dimension. This creates an artificial magnetic field, with the two coupled dimensions forming a Hall ribbon with sharp edges along the synthetic axis. We demonstrate that the large number of magnetic sublevels leads to distinct bulk and edge behaviours, and a Hall response characteristic of a non-trivial topology. We perform a preliminary investigation of the entanglement spectrum associated with a partition at the centre of the synthetic dimension, and we explain how future studies could directly implement the corresponding entanglement Hamiltonian. We conclude with a roadmap for extending the techniques presented in this thesis in order to realise many-body topological states.
The controlled, coherent manipulation of quantum-mechanical systems is an important challenge in modern science and engineering, with significant applications in quantum information science. Solid-state quantum systems such as electronic spins, nuclear spins, and superconducting islands are among the most promising candidates for realization of quantum bits (qubits). However, in contrast to isolated atomic systems, these solid-state qubits couple to a complex environment which often results in rapid loss of coherence, and, in general, is difficult to understand. Additionally, the strong interactions which make solid-state quantum systems attractive can typically only occur between neighboring systems, leading to difficulties in coupling arbitrary pairs of quantum bits. This thesis presents experimental progress in understanding and controlling the complex environment of a solid-state quantum bit, and theoretical techniques for extending the distance over which certain quantum bits can interact coherently. Coherent manipulation of an individual electron spin associated with a nitrogen-vacancy center in diamond is used to gain insight into its mesoscopic environment. Furthermore, techniques for exploiting coherent interactions between the electron spin and a subset of the environment are developed and demonstrated, leading to controlled