We construct the finite-temperature dynamical phase diagram of the fully connected transversefield Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics and exact diagonalization simulations are used to study the dynamics after a quantum quench in the system prepared in a thermal equilibrium state. The different dynamical phases characterized by the type of non-analyticities that emerge in an appropriately defined Loschmidt-echo return rate directly correspond to the dynamical phases determined by the spontaneous breaking of Z2 symmetry in the long-time steady state. The dynamical phase diagram is qualitatively different depending on whether the initial thermal state is ferromagnetic or paramagnetic. Whereas the former leads to a dynamical phase diagram that can be directly related to its equilibrium counterpart, the latter gives rise to a divergent dynamical critical temperature at vanishing final transverse-field strength.arXiv:1712.02175v3 [cond-mat.stat-mech]

The Loschmidt echo (LE) is a purely quantum-mechanical quantity whose determination for large quantum many-body systems requires an exceptionally precise knowledge of all eigenstates and eigenenergies. One might therefore be tempted to dismiss the applicability of any approximations to the underlying time evolution as hopeless. However, using the fully connected transverse-field Ising model (FC-TFIM) as an example, we show that this indeed is not the case, and that a simple semiclassical approximation to systems well described by mean-field theory (MFT) is in fact in good quantitative agreement with the exact quantum-mechanical calculation. Beyond the potential to capture the entire dynamical phase diagram of these models, the method presented here also allows for an intuitive geometric interpretation of the fidelity return rate at any temperature, thereby connecting the order parameter dynamics and the Loschmidt echo in a common framework. Videos of the post-quench dynamics provided in the supplemental material visualize this new point of view.Equilibrium phase transitions are remarkable phenomena that have been under thorough experimental and theoretical investigation for decades. Over time, a number of advanced techniques such as scaling theory [1-3] and the renormalization group method [4-9] have been developed for the determination of the universal properties close to a critical point. One might ask whether an indepth study of dynamical critical phenomena far from equilibrium is possible along the lines established in the equilibrium framework. With the advent of modern ultracold atom [10-13] and ion-trap [14-16] experiments, this originally purely academic question has become accessible in laboratories as well.Dynamical quantum phase transitions (DPTs) occur in the dynamics of a quantum system after quenching a set of control parameters {Γ} of its Hamiltonian:Recently, the study of DPTs has focused on two largely independent concepts [17]. The first one, , resembles equilibrium Landau theory: A system undergoes a dynamical phase transition if the long-time limit of the order parameter is finite for one set {Γ i , Γ f }, whereas it vanishes for different final parameters {Γ f }. Furthermore, DPT-I also entails criticality in the transient dynamics of the order parameter and two-point correlators before reaching the steady state, giving rise to effects such as dynamic scaling and aging, which have been investigated theoretically [30][31][32] and also observed experimentally [33].The second concept, DPT-II, generalizes the nonanalytic behavior of the free energy at a phase transition in the thermodynamic limit (TL) to the out-ofequilibrium case. To this end, the LE has been introduced as a dynamical analog of a free energy per particle [34]. DPT-II has been extensively studied both theoretically [34][35][36][37][38][39][40][41][42][43] and in experiments [44,45]. As we aim to calculate dynamical phase transitions at finite preparation temperatures, we define the distance covered in Hilbert space between the pr...

Here we report a method for improving the magnetic field sensitivity of an ensemble of Nitrogen-Vacancy (NV) centres in 12 C-enriched diamond aligned along the [111] crystal axis. The preferentially-aligned NV centres are fabricated by a Plasma Enhanced Chemical Vapour Deposition (PECVD) process and their concentration is quantitatively determined by analysing the confocal microscopy images. We further observe that annealing the samples at high temperature (1500 °C) in vacuum leads to a conversion of substitutional nitrogen into NV centres. This treatment also increases the coherence time of the NV centres electron spins up to 40 μs, which corresponds to enhancement of the sensitivity by a factor of three. However, this procedure also leads to a loss of the preferential alignment by 34%.

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