We propose to create and stabilize long-lived macroscopic quantum superposition states in atomic ensembles. We show that using a fully quantum parametric amplifier can cause the simultaneous decay of two atoms and, in turn, create stabilized atomic Schr\"{o}dinger cat states. Remarkably, even with modest parameters these intracavity atomic cat states can have an extremely long lifetime, up to \emph{4 orders of magnitude} longer than that of intracavity photonic cat states under the same parameter conditions, reaching \emph{tens of milliseconds}. This lifetime of atomic cat states is ultimately limited to \emph{several seconds} by extremely weak spin relaxation and thermal noise. Our work opens up a new way toward the long-standing goal of generating large-size and long-lived cat states, with immediate interests both in fundamental studies and noise-immune quantum technologies.
We analyze the symmetry properties of the dipolar Hamiltonian as the main relaxation mechanism responsible for the observed NMR spectra of long-lived states of methyl groups. Long-lived states exhibit relaxation times that are considerably longer than the spin–lattice relaxation time,
T1 . The analysis is complementary to previous studies and provides insight into the relaxation mechanism of long-lived states by focusing exclusively on the symmetry of the spin Hamiltonian. Our study shows that the dipole–dipole coupling between protons of a methyl group and between the protons and an external spin are both symmetry breaking interactions that can lead to relaxation pathways that transform the polarization from symmetry order to Zeeman order. The net contribution of the internal dipolar interaction to the NMR observation of long-lived states is zero. Our calculation is in good agreement with the reported features of the observed spectra and previous theoretical studies.
Delocalized long-lived states (LLSs) and collective zero-quantum long-lived coherences (LLCs) in aliphatic chains provide a promising route for preserving nuclear spin order with lifetimes that exceed the conventional
T1 and
T2 relaxation times, respectively. Their extended lifetimes make them attractive for applications including hyperpolarization storage, ligand-observed drug screening based on the loss of longevity upon binding to a target protein, and quantum information processing exploiting the collective properties of many-body spin systems. Although LLSs and LLCs have been observed experimentally in methylene networks, their origin and general structure in chains of arbitrary length have remained unclear. Here we show that these relaxation-protected modes follow directly from Redfield relaxation theory. Specifically, we construct the long-lived subspace, i.e., the zero-eigenvalue subspace of the relaxation superoperator associated with the dominant intra-pair dipole--dipole relaxation mechanism. The long-lived subspace contains
2N−1 independent non-trivial operators, which excludes the identity operator, where
N>1 is the number of
−CH2− groups in the chain. In achiral molecules, conservation of the global intra-pair permutation parity restricts experimental access to at most
2N−2 of these operators, whereas in chiral molecules this parity is not conserved, making up to
2N−1 long-lived operators accessible. We further develop a general framework for constructing both LLSs and LLCs in aliphatic chains containing an arbitrary number of
−CH2− groups in achiral molecules, and illustrate the approach explicitly for chains with
N=2, 3, and 4 methylene groups.