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Physical Review A

Effects of detuning on tunneling and traversal of ultracold atoms through vacuum-induced potentials

Fazal Badshah, Muhammad Irfan, Sajid Qamar, Shahid Qamar

Published Jan 31, 2013• 10 citations
Publisher

Abstract

In this paper, we study the tunneling and traversal of ultracold two-level atoms through the potential induced by the vacuum cavity mode. In particular, we discuss the effects of off-resonant interaction between the cavity mode and atomic transition on tunneling time of the ultracold atoms through a high-$Q$ mazer cavity. The phase time which may be considered as an appropriate measure of the time required for the atom to cross the cavity, exhibits some interesting features in the presence of off-resonant interaction. For example, switching between the sub and superclassical behaviors in phase time occurs for proper choice of detuning. Similarly, negative phase time appears for the transmission of atoms in both excited and ground states in the presence of off-resonant interaction.

DOI
10.1103/physreva.87.012132

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In this paper, we study the tunneling and traversal of ultracold two-level atoms through the potential induced by the vacuum cavity mode. In particular, we discuss the effects of off-resonant interaction between the cavity mode and atomic transition on tunneling time of the ultracold atoms through a high-QQQ mazer cavity. The phase time which may be considered as an appropriate measure of the time required for the atom to cross the cavity, exhibits some interesting features in the presence of off-resonant interaction. For example, switching between the sub and superclassical behaviors in phase time occurs for proper choice of detuning. Similarly, negative phase time appears for the transmission of atoms in both excited and ground states in the presence of off-resonant interaction.
Abstract We study the tunneling and traversal time of ultracold two-level atoms through a high quality microwave cavity containing N − 1 ground state atoms. The phase time of tunneling may be considered as a measure of the time required to traverse the cavity which exhibits both super and subclassical traversal behaviors. Here we examine that superclassical phase time behavior suppresses with the increase in the number of motionless ground state atoms inside the cavity. It happens due to the multipartite influence in the interaction that traps the incident atom into its upper state such that it does not observe any induced potential. Accordingly, for larger atomic samples, the incident atoms in the initial excited states get perfect transmission and tunnel through the cavity nearly with the same speed as they would have moved through a free space. This is true for any width of potential and the particle’s speed provided that the center-of-mass energy of the incident particle lies in the classically forbidden range.
Abstract We study the tunneling and traversal of ultracold three-level atoms through a high- Q microwave cavity. In particular, we analyzed effects of the atom-field detuning on the tunneling time of ultracold atoms through a two-photon mazer cavity. Here, photons are emitted and absorbed in pairs; therefore, the nature of the interaction is quite different from a single photon mazer. It is found that when an appropriate detuning is introduced, one may obtain alternate positive and negative values of the phase time of tunneling with increasing centre-of-mass energies of the incident atoms. Further, phase time can be switched between the sub- and super-classical characters, and its peak value may be smartly controlled by adjusting the atom-field detuning. More interestingly, we find that phase time rigorously depends on the internal degree of freedom of the interacting atoms, i.e. the final state in which the atoms are exiting the cavity.
We study the tunneling and traversal of ultracold $\ensuremath{\Lambda}$-type three-level atoms through vacuum-induced potentials in a high-QQQ mazer cavity. In particular, we discuss the effects of driving-induced atomic coherence on the passage of ultracold atoms through a high-QQQ mazer cavity. We consider phase time to study quantum tunneling which exhibits interesting features due to atomic coherence. For example, negative phase time appears for transmission of the atoms in both excited and ground states due to the presence of atomic coherence. Further, for certain values of the driving field, it is found that the phase tunneling time shows an alternate subclassical and superclassical traversal behavior with the increase in atomic momentum.
We examine the passage of ultracold two-level atoms through the potential produced by the vacuum of the cavity field. We find that the phase time may be considered as the appropriate measure of the time required for the atom to traverse the cavity. The phase tunneling time for ultracold atoms exhibits both super- and sub-classical time and we show how this behavior may be understood in terms of the momentum dependence of the phase of transmission amplitude. The passage of the atom through the cavity is unique, as it involves a coherent addition of the transition amplitudes corresponding to both barrier and well.
Abstract We study the tunneling time of ultracold V-type atoms interacting a high quality microwave cavity. Here atomic coherence is introduced in the system by a strong driving field which couples the two lower states of the three-level atom. It is found that in the presence of coherence, mazer action or the scattering like nature of the interaction may be examined for extended energies of the incident cold atoms. Our results show that position and amplitudes of the peak values of the phase time (traversal time) may be very effectively controlled by the coherent driving field. Further, here we obtained superclassical values of the phase time corresponding to much higher values of the transmission amplitudes of the tunneling atoms which may be advantageous in the possible experimental realization of the superclassical tunneling time of the traversing cold atoms. In addition, we examine a mirror reflection type symmetry in the phase time curve for a judicious choice of the external driving field .
We examine the traversal aspect of ultracold two-level atoms through a high-quality two-photon mazer with squeezed vacuum and coherent field distributions. Here the net cavity potential is constituted by the coherent addition of multiple barriers and well potentials, which is quite different from the potential offered by a cavity in the Fock or vacuum state. For squeezed vacuum and coherent field distributions, one gets different phase times ( t p h ) for different modes of the distribution, which are then averaged by taking the weighted mean on the t p h over the n-dependent transmission probability. It is found that the nature, intensity of the field, and injected coherence of the incident atoms have a decisive role in controlling peak values and sub- and superclassical traversals of the tunneling atoms. For two of the system’s dressed states ( | Φ b 0 ⟩ , | Φ b 1 ⟩ ), the cavity offers reflectionless transmission, as the atoms experience zero potential due to the dark state formation. Moreover, for a somewhat intense cavity field, mazer action (scattering-type behavior) may be obtained for an extended range of energies due to increased cavity potential in the course of atom–cavity interaction.