Carrier Envelope Phase Effect of a Long Duration Pulse in the Low Frequency Region

Using the characteristic of small energy difference between two high Rydberg states, we theoretically investigate the carrier envelope phase （CEP） effect in a bound-bound transition of an atom in a low-frequency long laser pulse with tens of optical cycles. Particularly, we first prepare a Rydberg state of a hydrogen-like atom by a laser field with the resonant frequency between this state and the ground state. Then by using a low-frequency long laser pulse interacting with this Rydberg atom, we calculate the population of another Rydberg state nearby this Rydberg state at the end of the laser pulse and find that the population changes dramatically with the CEP of the low-frequency pulse. This CEP effect is attributed to the interference between the positive-frequency and negative-frequency components in one-photon transition. These results may provide a method to measure the CEP value of a long laser pulse with low frequency.