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Hu'nan Shifan Daxue xuebao. Ziran kexue ban

Squeezing of Phonon Fields Induced by Coherence of Internal States of Trapped Ions

Zeng Hao-Sheng

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

While the frequency of classical driving filed is resonant to the redside band of center-of-mass mode and without Lamb-Dicke limit,the dynamics of the internal states of two trapped ions coupled to their phonon filed can be described by a nonlinear Jaynes-Cummings model.When the internal state of trapped ions is initially in a non-coherent mixed state and the phonon field in a vacuum state,the evolved state of the phonon field does not appear squeezing;However,when the internal state is initially in a coherent superposition pure state and the phonon field in a vacuum state,the evolved state of the phonon field shows squeezing.Under proper initial conditions,the squeezing is persistent and periodic in time.

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While the frequency of classical driving filed is resonant to the redside band of center-of-mass mode and without Lamb-Dicke limit,the dynamics of the internal states of two trapped ions coupled to their phonon filed can be described by a nonlinear Jaynes-Cummings model.When the internal state of trapped ions is initially in a non-coherent mixed state and the phonon field in a vacuum state,the evolved state of the phonon field does not appear squeezing;However,when the internal state is initially in a coherent superposition pure state and the phonon field in a vacuum state,the evolved state of the phonon field shows squeezing.Under proper initial conditions,the squeezing is persistent and periodic in time.
It is shown that two trapped ions interacting with laser beams resonant to the first red side-band of center-of-mass mode, in Lamb Dicke regime and under rotating wave approximation, is described by a Jaynes-Cummings model. For the initial condition that the motional state of centor-of-mass mode is in vacuum state and the internal state is prepared in a coherent superposition of states, coherence and squeezing for the vibratile motion of center-of-mass mode are discussed, particularly, a weak coherent state and a weak squeezed vacuum state are obtained. Collapse and revival are also observed in this type of initial condition.
It is shown that two trapped ions interacting with laser beams resonant to the first red side-band of center-of-mass mode, in Lamb Dicke regime and under rotating wave approximation, is described by a Jaynes-Cummingsmodel. For the initial condition that the motional state of center-of-mass mode is in vacuum state and the internal stateis prepared in a coherent superposition of states, coherence and squeezing for the vibratile motion of center-of-mass modeare discussed, particularly, a weak coherent state and a weak squeezed vacuum state are obtained. Collapse andrevival are also observed in this type of initial condition.
We showed that in Lamb-Dicke regime and under rotating wave approximation, the dynamical behavior of two trapped ions interacting with a laser beam resonant to the first red side-band of center-of-mass mode can be described by Jaynes-Cummings Model. An exact analytic solution for this kind of Jaynes-Cummings model is presented. The results showed that quantum collapses and revivals for the occupation of two atoms, and squeezing for vibratic motion of center-of-mass mode existed in both two different types of initial conditions. The maximum momentum squeezing for center-of-mass mode in these two types of conditions are found to be 42.4% and 43.8% respectively. The coherence, in the first type of initial conditions can keeps long times, and in the second type of initial conditions, a concrete form of coherent state is obtained, when the initial average number is very small.
We present a theoretical model for realizing squeezed lasing in a trapped-ion system without relying on engineered baths or tailored dissipative reservoirs. Our approach leverages the intrinsic ion-phonon interactions, where two trapped ions, each interacting with a shared vibrational mode, are driven on both red- and blue-sideband transitions. This enables the creation of a squeezed state of motion through the dynamic coupling between the ions' internal states and the phonon mode. Unlike traditional methods that require bath engineering, our model demonstrates that squeezed lasing can be achieved through a direct manipulation of ion-phonon interactions, with no external reservoirs required. We explore the steady-state behavior of the system, analyzing the onset of lasing, gain-loss balance, and the role of the squeezing parameter in shaping the phonon field's statistical properties. Furthermore, we show how external coherent drives can stabilize phase coherence and achieve controlled quadrature squeezing, offering a simple yet effective method for achieving squeezed lasing in quantum mechanical systems. Our findings provide new insights into the realization of squeezed states in phonon-based systems, with potential applications in quantum metrology and information processing.
Starting from the Jaynes-Cummings(J-C) model describing the interaction of a trapped ion with a standing wave laser field,we derive the interaction Hamiltonian on the nonlinear J-C model of the trapped ion excited resonantly with single quantum vibrational mode.After solving the time dependent states of this model,we study the ion centroid motion of squeezing effects by utilizing the ion numerical model.It is shown that the ion squeezing effects is related with the Lamb-Dicke parameter and the position of the ion in the standing wave laser field.