arXiv subjects
Publications and source records attributed to Bryan J. Dalton.
We determine the form of the unitary transformation that diagonalizes the Jaynes-Cummings Hamiltonian. This leads to operators the action of which has a simple interpretation in terms of the dressed states, the energy eigenstates. This suggests a set of coherent states and spin coherent states based on the dressed states.
We show that interacting bosons on a ring which are driven periodically by a rotating potential can support discrete time crystals whose absolute stability can be proven. The absolute stability is demonstrated by an exact mapping of discrete time crystal states to low-lying eigenstates of a time-independent model that reveals spontaneous breaking of space translation symmetry. The mapping ensures that there are no residual time-dependent terms that could lead to heating of the system and destruction of discrete time crystals. We also analyze periodically kicked bosons where the mapping is approximate only and cannot guarantee the absolute stability of discrete time crystals. Besides illustrating potential sources of instability, the kicked bosons model demonstrates a rich field for investigating the interplay between different time and space symmetry breaking, as well as the stability of time crystal behavior in contact with a thermal reservoir.
The Glauber-Sudarshan P-representation is well-known within quantum optics, and is widely applied to problems involving photon statistics. Less familiar, perhaps, is its fermionic counterpart. We present a derivation of both the bosonic and fermionic distributions and, in doing so, demonstrate the reason for the existence of two distinct fermionic forms and the relationship between these. We consider both single mode systems and also multiparticle systems with many modes. For simplicity only one type of boson or fermion will be considered.
Discrete time crystals (DTCs) refer to a novel many-body steady state that spontaneously breaks the discrete time-translational symmetry in a periodically-driven quantum system. Here, we study DTCs in a Bose-Einstein condensate (BEC) bouncing resonantly on an oscillating mirror, using a two-mode model derived from a standard quantum field theory. We investigate the validity of this model and apply it to study the long-time behavior of our system. A wide variety of initial states based on two Wannier modes are considered. We find that in previous studies the investigated phenomena in the evolution time-window ($\lessapprox$2000 driving periods) are actually "short-time" transient behavior though DTC formation signaled by the sub-harmonic responses is still shown if the inter-boson interaction is strong enough. After a much longer (about 20 times) evolution time, initial states with no "long-range" correlations relax to a steady state, where time-symmetry breaking can be unambiguously defined. Quantum revivals also eventually occur. This long-time behavior can be understood via the many-body Floquet quasi-eigenenergy spectrum of the two-mode model. A symmetry-breaking edge for DTC formation appears in the spectrum for strong enough interaction, where all quasi-eigenstates below the edge are symmetry-breaking while those above the edge are symmetric. The late-time steady state's time-translational symmetry depends solely on whether the initial energy is above or below the symmetry-breaking edge. A phase diagram showing regions of symmetry-broken and symmetric phases for differing initial energies and interaction strengths is presented. We find that according to this two-mode model, the discrete time crystal survives for times out to at least 250,000 driving periods.
We show how one can prepare and detect entanglement and Einstein-Podolsky-Rosen (EPR) steering between two distinguishable groups (modes) of atoms in a Bose-Einstein condensate (BEC) atom interferometer. Our paper extends previous work that developed criteria for two-mode entanglement and EPR steering based on the reduced variances of two spins defined in a plane. Observation of planar spin squeezing will imply entanglement, and sufficient planar spin squeezing implies EPR steering, between the two groups of atoms. By using a two-mode dynamical model to describe BEC interferometry experiments, we show that the two-mode entanglement and EPR steering criteria are predicted to be satisfied for realistic parameters. The reported observation of spin squeezing in these parameter regimes suggests it is very likely that the criteria can be used to infer an EPR steering between mesoscopic groups of atoms, provided the total atom number can be determined to sub-Poissonian uncertainty. The criteria also apply to a photonic Mach-Zehnder interferometer. Finally, we give a method based on the amount of planar spin squeezing to determine a lower bound on the number of particles that are genuinely comprise the two-mode EPR steerable state - the so-called two-mode EPR steering depth.
This paper shows that phase space methods using a positive P type distribution function involving both c-number variables (for the cavity mode) and Grassmann variables (for the two level atom) can be used to treat the Jaynes-Cummings model. Although it is a Grassmann function, the distribution function is equivalent to six c-number functions of the two bosonic variables. Experimental quantities are given as bosonic phase space integrals involving the six functions. A Fokker-Planck equation involving both left and right Grassmann differentiation can be obtained for the distribution function, and is equivalent to six coupled equations for the six c-number functions. The approach used involves choosing the canonical form of the (non-unique) positive P distribution function, where the correspondence rules for bosonic operators are non-standard and hence the Fokker-Planck equation is also unusual. Initial conditions, such as for initially uncorrelated states, are used to determine the initial distribution function. Transformations to new bosonic variables rotating at the cavity frequency enables the six coupled equations for the new c-number functions (also equivalent to the canonical Grassmann distribution function) to be solved analytically, based on an ansatz from a 1980 paper by Stenholm. It is then shown that the distribution function is the same as that determined from the well-known solution based on coupled equations for state vector amplitudes of atomic and n-photon product states. The treatment of the simple two fermion mode Jaynes-Cummings model is a useful test case for the future development of phase space Grassmann distribution functional methods for multi-mode fermionic applications in quantum-atom optics.