A system consisting of a number of trapped two-level atoms in the presence of external inhomogeneous magnetic field undergoes dephasing: classically, since each atom feels a different field along its trajectory, the pseudospin rotation rates differ; as a result the average spin decays. It has been demonstrated in recent years that in the case of systems initiated in the atomic coherent state such spin dephasing can be prevented by tuning the interaction between the atoms to induce so-called spin self-rephasing. While the effect has been studied theoretically from a semiclassical point of view, a quantum-mechanical description is limited. In this paper we provide a numerical simulation of an ab initio model and provide realistic examples of spin self-rephasing used to counteract the effect of inhomogeneous magnetic field. We found that the spin self-rephasing method can be also used to prevent atomic squeezed states from decoherence: while the dephasing inhibition is lower as compared with the case of coherent states, it is still comparatively large and may be useful in real interferometric scenarios.
A system consisting of a number of trapped two-level atoms in the presence of external inhomogeneous magnetic field undergoes dephasing: classically, since each atom feels a different field along its trajectory, the pseudospin rotation rates differ; as a result the average spin decays. It has been demonstrated in recent years that in the case of systems initiated in the atomic coherent state such spin dephasing can be prevented by tuning the interaction between the atoms to induce so-called spin self-rephasing. While the effect has been studied theoretically from a semiclassical point of view, a quantum-mechanical description is limited. In this paper we provide a numerical simulation of an ab initio model and provide realistic examples of spin self-rephasing used to counteract the effect of inhomogeneous magnetic field. We found that the spin self-rephasing method can be also used to prevent atomic squeezed states from decoherence: while the dephasing inhibition is lower as compared with the case of coherent states, it is still comparatively large and may be useful in real interferometric scenarios.
We investigate the collective spin dynamics of a self-rephasing bosonic ensemble of 87Rb trapped in a one-dimensional vertical optical lattice. We show that the combination of the frequency shifts induced by atomic interactions and inhomogeneous dephasing, together with the spin self-rephasing mechanism, leads to the existence of a ``magic density'': i.e., a singular operating point where the clock transition is first-order insensitive to density fluctuations. This feature is very appealing for improving the stability of quantum sensors based on trapped pseudo-spin-1/2 ensembles. Ramsey spectroscopy of the $|5s{\phantom{\rule{3.33333pt}{0ex}}}^{2}{S}_{1/2},F=1,{m}_{F}=0\ensuremath{\rangle}\ensuremath{\rightarrow}|5s{\phantom{\rule{3.33333pt}{0ex}}}^{2}{S}_{1/2},F=2,{m}_{F}=0\ensuremath{\rangle}$ hyperfine transition is in qualitative agreement with a numerical model based on coupled Bloch equations of motion for energy-dependent spin vectors.
We examine the time evolution of cold atoms (impurities) interacting with an environment consisting of a degenerate bosonic quantum gas. The impurity atoms differ from the environment atoms, being of a different species. This allows one to superimpose two independent trapping potentials, each being effective only on one atomic kind, while transparent to the other. When the environment is homogeneous and the impurities are confined in a potential consisting of a set of double wells, the system can be described in terms of an effective spin-boson model, where the occupation of the left or right well of each site represents the two (pseudo)-spin states. The irreversible dynamics of such system is here studied exactly, i.e. not in terms of a Markovian master equation. The dynamics of one and two impurities is remarkably different in respect of the standard decoherence of the spin-boson system. In particular, we show: (i) the appearance of coherence oscillations, (ii) the presence of super and subdecoherent states that differ from the standard ones of the spin-boson model, and (iii) the persistence of coherence in the system at long times. We show that this behaviour is due to the fact that the pseudospins have an internal spatial structure. We argue that collective decoherence also prompts information about the correlation length of the environment. In a one-dimensional (1D) configuration, one can change even more strongly the qualitative behaviour of the dephasing just by tuning the interaction of the bath.
We present a detailed analysis of spin squeezing of the one-axis twisting model with a many-body phase dephasing, which is induced by external field fluctuation in a two-mode Bose-Einstein condensates. Even in the presence of the dephasing, our analytical results show that the optimal initial state corresponds to a coherent spin state ∣θ0,ϕ0⟩ with the polar angle θ0=π/2. If the dephasing rate γ≪S−1/3, where S is total atomic spin, we find that the smallest value of squeezing parameter (i.e., the strongest squeezing) obeys the same scaling with the ideal one-axis twisting case, namely ξ2∝S−2/3. While for a moderate dephasing, the achievable squeezing obeys the power rule S−2/5, which is slightly worse than the ideal case. When the dephasing rate γ>S1/2, we show that the squeezing is weak and neglectable.
Motivated by the spin self-rephasing recently observed in an atomic clock, we introduce a simple dynamical model to study the competition between dephasing and synchronization. Two spins S are taken to be initially parallel and in the plane perpendicular to an inhomogeneous magnetic field Δ that tends to dephase them. In addition, the spins are coupled by exchange interaction J that tries to keep them locked. The analytical solution of the classical dynamics shows that there is a phase transition to a synchronized regime for sufficiently large exchange interaction compared to the inhomogeneity. The quantum dynamics is solved analytically in four limits —large/small and large/small S — and numerically in between. In sharp contrast to the classical case, the quantum solution features very rich S -dependent multiscale dynamics. For any finite S , there is no synchronization but a crossover around between two regimes. The synchronization transition is only recovered when , approaching the classical solution in a non-trivial way. Quantum effects therefore suppress the synchronization transition.
Motivated by the spin self-rephasing recently observed in an atomic clock, we introduce a simple dynamical model to study the competition between dephasing and synchronization. Two spins S are taken to be initially parallel and in the plane perpendicular to an inhomogeneous magnetic field Δ that tends to dephase them. In addition, the spins are coupled by exchange interaction J that tries to keep them locked. The analytical solution of the classical dynamics shows that, there is a phase transition to a synchronized regime for sufficiently large exchange interaction J>Δ compared to the inhomogeneity. The quantum dynamics is solved analytically in four limits -- large/small J/Δ and large/small S -- and numerically in between. In sharp contrast to the classical case, the quantum solution features very rich S-dependent multiscale dynamics. For any finite S, there is no synchronization but a crossover around J=Δ between two regimes. The synchronization transition is only recovered when S→∞, approaching the classical solution in a non-trivial way. Quantum effects therefore suppress the synchronization transition.
We investigate the role of interatomic interactions when a Bose gas, in a double-well potential with a finite tunneling probability (a ‘Bose–Josephson junction’), is exposed to external noise. We examine the rate of decoherence of a system initially in its ground state with equal probability amplitudes in both sites. The noise may induce two kinds of effects: firstly, random shifts in the relative phase or number difference between the two wells and secondly, loss of atoms from the trap. The effects of induced phase fluctuations are mitigated by atom–atom interactions and tunneling, such that the dephasing rate may be suppressed by half its single-atom value. Random fluctuations may also be induced in the population difference between the wells, in which case atom–atom interactions considerably enhance the decoherence rate. A similar scenario is predicted for the case of atom loss, even if the loss rates from the two sites are equal. We find that if the initial state is number-squeezed due to interactions, then the loss process induces population fluctuations that reduce the coherence across the junction. We examine the parameters relevant for these effects in a typical atom chip device, using a simple model of the trapping potential, experimental data, and the theory of magnetic field fluctuations near metallic conductors. These results provide a framework for mapping the dynamical range of barriers engineered for specific applications and set the stage for more complex atom circuits (‘atomtronics’).