Optimal Phase Sensing in Trapped Ions with One-Axis-Twisting Hamiltonian

The properties of model fluids are investigated, whose particles have classical degrees of freedom in two and three dimensions and two internal quantum states. Attractive interactions are ‘‘turned on,’’ when the internal states are hybridized, corresponding to molecules acquiring a ‘‘dipole’’ moment. The phase diagram of this system in the temperature‐density plane as well as the static and imaginary time correlations at various densities are investigated by path integral Monte Carlo simulations. These are compared with mean field theory predictions.

1)We investigate the properties of a model fluid whose molecules have classical degrees of freedom in two dimensions and two internal quantum states. The attractive interactions are “turned on” when the internal states are hybridized, corresponding to the molecules acquiring a “dipole” moment. The phase diagram of this system in the temperature- density plane is investigated by a combination of path integral Monte Carlo and block size analysis techniques. The results are compared with mean- field—theory predictions. 2) We present molecular dynamics simulation results of quenches into the unstable region of a two-dimensional Lennard-Jones system. The evolution of the system from the non-equilibrium state into equilibrium was analyzed with a dynamical block analysis.

In fringe projection profilometry, phase sensitivity is one of the important factors affecting measurement accuracy. A typical fringe projection system consists of one camera and one projector. To gain insight into its phase sensitivity, we perform in this paper a strict analysis in theory about the dependence of phase sensitivities on fringe directions. We use epipolar geometry as a tool to derive the relationship between fringe distortions and depth variations of the measured surface, and further formularize phase sensitivity as a function of the angle between fringe direction and the epipolar line. The results reveal that using the fringes perpendicular to the epipolar lines enables us to achieve the maximum phase sensitivities, whereas if the fringes have directions along the epipolar lines, the phase sensitivities decline to zero. Based on these results, we suggest the optimal fringes being circular-arc-shaped and centered at the epipole, which enables us to give the best phase sensitivities over the whole fringe pattern, and the quasi-optimal fringes, being straight and perpendicular to the connecting line between the fringe pattern center and the epipole, can achieve satisfyingly high phase sensitivities over whole fringe patterns in the situation that the epipole locates far away from the fringe pattern center. The experimental results demonstrate that our analyses are practical and correct, and that our optimized fringes are effective in improving the phase sensitivities and, further, the measurement accuracies.

Polyatomic molecules have rich structural features that make them uniquely suited to applications in quantum information science1-3, quantum simulation4-6, ultracold chemistry7 and searches for physics beyond the standard model8-10. However, a key challenge is fully controlling both the internal quantum state and the motional degrees of freedom of the molecules. Here we demonstrate the creation of an optical tweezer array of individual polyatomic molecules, CaOH, with quantum control of their internal quantum state. The complex quantum structure of CaOH results in a non-trivial dependence of the molecules' behaviour on the tweezer light wavelength. We control this interaction and directly and non-destructively image individual molecules in the tweezer array with a fidelity greater than 90%. The molecules are manipulated at the single internal quantum state level, thus demonstrating coherent state control in a tweezer array. The platform demonstrated here will enable a variety of experiments using individual polyatomic molecules with arbitrary spatial arrangement.

In this paper, we study the preparation and nondestructive analysis of photon and spin entangled states with double-sided cavity and nitrogen-vacancy center coupled system, which is efficient in weak-coupling regime. The setups are based on some simple linear optical elements, delay lines and conventional photon detectors, which are feasible with existing experimental technology. Numerical simulation demonstrates that all protocols’ fidelities and successful probabilities are high in principle. Therefore, our protocols may be useful for decreasing the experimental requirements for preparation and nondestructive analysis of entangled states.

A model molecular fluid with two-dimensional classical degrees of freedom and two internal quantum states is studied by path integral Monte Carlo simulations. The temperature-density phase diagram is obtained to a high degree of precision using finite-size scaling techniques and local structure analysis methods. We locate the phase boundaries of gas, liquid, square and hexagonal lattice solid phases together with a preferred internal quantum state resulting in tricritical and triple points. The simulation results for the liquid-solid transitions are compared with recent density functional theory calculations.

We present simulation results on phase transitions in a fluid system whose interactions depend on internal quantum states: they are ``turned on'' when the molecules are in a hybrid state. Surprisingly, a simple effective temperature-dependent classical potential describes well many features of the transition.

The concept of local structure in fluids is applied to a complex model fluid with classical translations in two dimensions and two internal quantum states. We demonstrate the usefulness and efficiency of an analysis based on local structure parameters that allows us to locate the liquid-solid transition density from configurations generated by standard constant-volume simulations. Our findings are in close agreement with recent predictions from a density-functional treatment of this freezing transition. In addition to these methodological aspects, open questions concerning the conjectured existence of two triple points in the two-dimensional fluid with internal quantum states can be settled.

When two particles, atoms or polyatomic molecules, collide there is always a possibility that one outcome of the event will be a redistribution of the energy contained in the internal structure of either or both collision partners. Such molecular encounters are called inelastic collisions to distinguish them from their less complicated elastic collision companions, in which no such redistributions of internal energy take place. Elastic collisions conserve all of the external manifestations of molecular presence, namely molecular mass, molecular momentum and molecular translational energy and, in addition, they conserve the identities of the two collision partners. Inelastic collisions also preserve mass and momentum but, where energy is concerned, it is the sum of molecular translational and internal energies that is preserved. Insofar as an inelastic collision between a pair of molecules may result in the emergence from the encounter of two molecules that are chemically totally different from the original incident pair, it is clear that inelastic encounters may not preserve identity. Indeed if one molecule is identified by both its chemical type and by its internal quantum state it can be said that identity is always lost in an inelastic collision, since internal quantum state must change when internal energy is exchanged in an encounter.

A model fluid whose molecules have classical degrees of freedom in 2D and two internal quantum states is studied by path-integral Monte Carlo simulation. We obtain a rich phase diagram including phase coexistences and tricritical and triple points with high precision by combining for the first time block-analysis finite-size scaling ideas with quantum Monte Carlo simulations. We find a square lattice solid phase in coexistence with gas and/or liquid phases. Compressibilities and susceptibilities are compared to mean-field predictions and low-density expansions.

Multiparticle entanglement enables quantum simulations, quantum computing, and quantum-enhanced metrology. Yet, there are few methods to produce and measure such entanglement while maintaining single-qubit resolution as the number of qubits is scaled up. Using atom chips and fiber-optical cavities, we have developed a method based on nondestructive collective measurement and conditional evolution to create symmetric entangled states and perform their tomography. We demonstrate creation and analysis of entangled states with mean atom numbers up to 41 and experimentally prove multiparticle entanglement. Our method is independent of atom number and should allow generalization to other entangled states and other physical implementations, including circuit quantum electrodynamics.

ABSTRACTAtoms and molecules often react at different rates depending on their internal quantum states. Thus, controlling which internal states are populated can be used to manipulate the reactivity and can lead to a more detailed understanding of reaction mechanisms. We demonstrate this control of reactions by studying the electronically excited state reaction . This reaction is exothermic only if Ca is in one of its excited electronic states. Using laser-cooling and electrodynamic trapping, we cool and trap Ca at millikelvin temperatures for several minutes. We can then change the fraction of time they spend in each of the two excited states by adjusting the detunings of the cooling lasers. This allows us to disentangle the reactions that begin with Ca in the 2P-state from the ones where Ca is in the 2D-state. Using time-of-flight mass spectrometry, we determine independent reaction rate constants for Ca in both electronically excited states.

Chapter 6 - Detailed rate constants

We continue our investigation of the properties of a model fluid whose molecules have classical translational degrees of freedom and two quantum internal states. The attractive pair interactions are ``turned on'' when the internal states are hybridized, corresponding to the molecules acquiring a ``dipole'' moment. The phase diagram of this system in the temperature-density plane as well as the static and imaginary-time correlations at various densities are investigated by Monte Carlo simulations, using the ``polymer'' representation, for different strengths of the quantum parameter. These are compared with low-density expansions and mean-field-theory predictions. Good agreement is found in appropriate regimes.

We investigate the systematic use of the Schwinger representation, by virtue of which two boson fields are equivalent to an effective spin, for casting multimode squeezed states into multipartite spin entangled states. The motivation for this endeavor is the following established fact: finitely squeezed, two-mode entangled states can be recast into maximally entangled bipartite spin states, irrespective of their level of squeezing (in the lossless case). This work explores the generalization of this interesting property to multipartite entanglement. While we found that the generalization of multipartite Gaussian entanglement to multipartite spin entanglement is not straightforward, there are nonetheless interesting features and entangled states to be found. Here we study a few CV entangled states already realized experimentally, and show that some of them correspond to multipartite spin entangled states.