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Register a new userNon-adiabatic generation of NOON states in a Tonks--Girardeau gas
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With adiabatic techniques, it is possible to create quantum superposition states with high fidelity while exercising limited control over the parameters of a system. However, because these techniques are slow compared to other timescales in the system, they are usually not suitable for creating highly unstable states or performing time-critical processes. Both of these situations arise in quantum information processing, where entangled states may only be isolated from the environment for a short time and where quantum computers require high-fidelity operations to be performed quickly. Recently it has been shown that techniques like optimal control and shortcuts to adiabaticity may be used to prepare quantum states non-adiabatically with high fidelity. Here we present two examples of how these techniques can be used to create maximally entangled many-body NOON states in one-dimensional Tonks--Girardeau gases.
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A harmonically trapped ultracold 1D spin-1 Bose gas with strongly repulsive or attractive 1D even-wave interactions induced by a 3D Feshbach resonance is studied. The exact ground state, a hybrid of Tonks-Girardeau (TG) and ideal Fermi gases, is constructed in the TG limit of infinite even-wave repulsion by a spinor Fermi-Bose mapping to a spinless ideal Fermi gas. It is then shown that in the limit of infinite even-wave attraction this same state remains an exact many-body eigenstate, now highly excited relative to the collapsed generalized McGuire cluster ground state, showing that the hybrid TG state is completely stable against collapse to this cluster ground state under a sudden switch from infinite repulsion to infinite attraction. It is shown to be the TG limit of a hybrid super Tonks-Girardeau (STG) state which is metastable under a sudden switch from finite but very strong repulsion to finite but very strong attraction. It should be possible to create it experimentally by a sudden switch from strongly repulsive to strongly attractive interaction, as in the recent Innsbruck experiment on a spin-polarized bosonic STG gas. In the case of strong attraction there should also exist another STG state of much lower energy, consisting of strongly bound dimers, a bosonic analog of a recently predicted STG gas which is an ultracold gas of strongly bound bosonic dimers of fermionic atoms, but it is shown that this STG state cannot be created by such a switch from strong repulsion to strong attraction.
We propose a scheme for generating atomic NOON states via adiabatic passage. In the scheme, a double $Lambda$-type three-level atom is trapped in a bimodal cavity and two sets of $Lambda$-type three-level atoms are translated into and outside of two single mode cavities respectively. The three cavities connected by optical fibres are always in vacuum states. After a series of operations and suitable interaction time, we can obtain arbitrary large-$n$ NOON states of two sets of $Lambda$-type three-level atoms in distant cavities by performing a single projective measurement on the double $Lambda$-type three-level atom. Due to adiabatic elimination of atomic excited states and the application of adiabatic passage, our scheme is robust against the spontaneous emissions of atoms, the decays of fibres and cavities photon leakage. So the scheme has a high fidelity and feasibility under the current available techniques.
Strongly correlated states in many-body systems are traditionally created using elastic interparticle interactions. Here we show that inelastic interactions between particles can also drive a system into the strongly correlated regime. This is shown by an experimental realization of a specific strongly correlated system, namely a one-dimensional molecular Tonks-Girardeau gas.
We investigate the propagation of spin impurity atoms through a strongly interacting one-dimensional Bose gas. The initially well localized impurities are accelerated by a constant force, very much analogous to electrons subject to a bias voltage, and propagate as a one-dimensional impurity spin wave packet. We follow the motion of the impurities in situ and characterize the interaction induced dynamics. We observe a very complex non-equilibrium dynamics, including the emergence of large density fluctuations in the remaining Bose gas, and multiple scattering events leading to dissipation of the impuritys motion.
A harmonically trapped ultracold 1D spinor Fermi gas with a strongly attractive 1D even-wave interaction induced by a 3D Feshbach resonance is studied. It is shown that it has two different super Tonks-Girardeau (sTG) energy eigenstates which are metastable against collapse in spite of the strong attraction, due to their close connection with 1D hard sphere Bose gases which are highly excited gas-like states. One of these sTG states is a hybrid between an sTG gas with strong $(uparrowdownarrow$ attractions and an ideal Fermi gas with no $(uparrowuparrow)$ or $(downarrowdownarrow)$ interactions, the sTG component being an exact analog of the recently observed sTG state of a 1D ultracold Bose gas. It should be possible to create it experimentally by a sudden switch of the $(uparrowdownarrow)$ interaction from strongly repulsive to strongly attractive, as in the recent Innsbruck experiment on the bosonic sTG gas. The other is a trapped analog of a recently predicted sTG state which is an ultracold gas of strongly bound $(uparrowdownarrow)$ fermion dimers which behave as bosons with a strongly attractive boson-boson interaction leading to sTG behavior. It is proved that the probability of a transition from the ground state for strongly repulsive interaction to this dimer state under a sudden switch from strongly repulsive to strongly attractive interaction is $ll 1$, contrary to a previous suggestion.
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