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Dynamical quantum jumps were initially conceived by Bohr as objective events associated with the emission of a light quantum by an atom. Since the early 1990s they have come to be understood as being associated rather with the detection of a photon by a measurement device, and that different detection schemes result in different types of jumps (or diffusion). Here we propose experimental tests to rigorously prove the detector-dependence of the stochastic evolution of an individual atom. The tests involve no special preparation of the atom or field, and the required efficiency can be as low as eta ~58%.
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We analyze a special class of 1-D quantum walks (QWs) realized using optical multi-ports. We assume non-perfect multi-ports showing errors in the connectivity, i.e. with a small probability the multi- ports can connect not to their nearest neighbor but to another multi-port at a fixed distance - we call this a jump. We study two cases of QW with jumps where multiple displacements can emerge at one timestep. The first case assumes time-correlated jumps (static disorder). In the second case, we choose the positions of jumps randomly in time (dynamic disorder). The probability distributions of position of the QW walker in both instances differ significantly: dynamic disorder leads to a Gaussian-like distribution, while for static disorder we find two distinct behaviors depending on the parity of jump size. In the case of even-sized jumps, the distribution exhibits a three-peak profile around the position of the initial excitation, whereas the probability distribution in the odd case follows a Laplace-like discrete distribution modulated by additional (exponential) peaks for long times. Finally, our numerical results indicate that by an appropriate mapping an universal functional behavior of the variance of the long-time probability distribution can be revealed with respect to the scaled average of jump size.
We present a model for decoherence in time-dependent transport. It boils down into a form of wave function that undergoes a smooth stochastic drift of the phase in a local basis, the Quantum Drift (QD) model. This drift is nothing else but a local energy fluctuation. Unlike Quantum Jumps (QJ) models, no jumps are present in the density as the evolution is unitary. As a first application, we address the transport through a resonant state $leftvert 0rightrangle $ that undergoes decoherence. We show the equivalence with the decoherent steady state transport in presence of a B{u}ttikers voltage probe. In order to test the dynamics, we consider two many-spin systems whith a local energy fluctuation. A two-spin system is reduced to a two level system (TLS) that oscillates among $leftvert 0rightrangle $ $equiv $ $ leftvert uparrow downarrow rightrangle $ and $leftvert 1rightrangle equiv $ $leftvert downarrow uparrow rightrangle $. We show that QD model recovers not only the exponential damping of the oscillations in the low perturbation regime, but also the non-trivial bifurcation of the damping rates at a critical point, i.e. the quantum dynamical phase transition. We also address the spin-wave like dynamics of local polarization in a spin chain. The QD average solution has about half the dispersion respect to the mean dynamics than QJ. By evaluating the Loschmidt Echo (LE), we find that the pure states $leftvert 0rightrangle $ and $leftvert 1right rangle $ are quite robust against the local decoherence. In contrast, the LE, and hence coherence, decays faster when the system is in a superposition state. Because its simple implementation, the method is well suited to assess decoherent transport problems as well as to include decoherence in both one-body and many-body dynamics.
We introduce a first-order quantum-phase-transition model, which exhibits giant sensitivity $chi propto N^2$ at the critical point. Exploiting this effect, we propose a quantum critical detector (QCD) to amplify weak input signals. The time-dynamic QCD functions by triggering a first-order dynamical quantum phase transition in a system of spins with long-range interactions coupled to a bosonic mode. We numerically demonstrate features of the dynamical quantum phase transition, which leads to a time-dependent quantum gain. We also show the linear scaling with the spin number $N$ in both the quantum gain and the corresponding signal-to-quantum noise ratio of this QCD. Our QCD can be a resource for metrology, weak signal amplification, and single photon detection.
We consider a harmonic oscillator (HO) with a time dependent frequency which undergoes two successive abrupt changes. By assumption, the HO starts in its fundamental state with frequency omega_{0}, then, at t = 0, its frequency suddenly increases to omega_{1} and, after a finite time interval tau, it comes back to its original value omega_{0}. Contrary to what one could naively think, this problem is a quite non-trivial one. Using algebraic methods we obtain its exact analytical solution and show that at any time t > 0 the HO is in a squeezed state. We compute explicitly the corresponding squeezing parameter (SP) relative to the initial state at an arbitrary instant and show that, surprisingly, it exhibits oscillations after the first frequency jump (from omega_{0} to omega_{1}), remaining constant after the second jump (from omega_{1} back to omega_{0}). We also compute the time evolution of the variance of a quadrature. Last, but not least, we calculate the vacuum (fundamental state) persistence probability amplitude of the HO, as well as its transition probability amplitude for any excited state.
Quantum error correction (QEC) is required for a practical quantum computer because of the fragile nature of quantum information. In QEC, information is redundantly stored in a large Hilbert space and one or more observables must be monitored to reveal the occurrence of an error, without disturbing the information encoded in an unknown quantum state. Such observables, typically multi-qubit parities such as <XXXX>, must correspond to a special symmetry property inherent to the encoding scheme. Measurements of these observables, or error syndromes, must also be performed in a quantum non-demolition (QND) way and faster than the rate at which errors occur. Previously, QND measurements of quantum jumps between energy eigenstates have been performed in systems such as trapped ions, electrons, cavity quantum electrodynamics (QED), nitrogen-vacancy (NV) centers, and superconducting qubits. So far, however, no fast and repeated monitoring of an error syndrome has been realized. Here, we track the quantum jumps of a possible error syndrome, the photon number parity of a microwave cavity, by mapping this property onto an ancilla qubit. This quantity is just the error syndrome required in a recently proposed scheme for a hardware-efficient protected quantum memory using Schr{o}dinger cat states in a harmonic oscillator. We demonstrate the projective nature of this measurement onto a parity eigenspace by observing the collapse of a coherent state onto even or odd cat states. The measurement is fast compared to the cavity lifetime, has a high single-shot fidelity, and has a 99.8% probability per single measurement of leaving the parity unchanged. In combination with the deterministic encoding of quantum information in cat states realized earlier, our demonstrated QND parity tracking represents a significant step towards implementing an active system that extends the lifetime of a quantum bit.
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