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arXiv:1005.1259 · Physical Review A

State-insensitive bichromatic optical trapping

Bindiya Arora, Marianna S. Safronova, Charles W. Clark

Published Aug 19, 2010• 15 citations
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Abstract

We study a scheme for state-insensitive trapping of neutral atoms by using light with two independent wavelengths. In particular, we describe the use of trapping and control lasers to minimize the variance of the potential experienced by a trapped Rb atom in ground and excited states. We present calculated values of wavelength pairs for which the $5s$ and $5{p}_{3/2}$ levels have the same ac Stark shifts in the presence of two laser fields.

DOI
10.1103/physreva.82.022509

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arXiv:1008.3856•Physical Review A•Dec 30, 2010•59 citations
We study a scheme for state-insensitive trapping of neutral atoms by using light with two independent wavelengths. In particular, we describe the use of trapping and control lasers to minimize the variance of the potential experienced by a trapped Rb atom in ground and excited states. We present calculated values of wavelength pairs for which the 5s5s5s and 5p3/25{p}_{3/2}5p3/2​ levels have the same ac Stark shifts in the presence of two laser fields.
State-insensitive dipole trapping of multilevel atoms can be achieved by an appropriate choice of the wavelength of the trapping laser, so that the interaction with the different transitions results in equal AC Stark shifts for the ground and excited states of interest. However this approach is severely limited by the availability of coherent sources at the required wavelength and of appropriate power. This work investigates state-insensitive trapping of caesium atoms for which the required wavelength of 935.6 nm is inconvenient in terms of experimental realization. Bichromatic state-insensitive trapping is proposed to overcome the lack of suitable laser sources. We first consider pairs of laser wavelengths in the ratio 1:2 and 1:3, as obtained via second- and third- harmonic generation. We found that the wavelength combinations 931.8-1863.6 nm and 927.5-2782.5 nm are suitable for state-insensitive trapping of caesium atoms. In addition, we examine bichromatic state-insensitive trapping produced by pairs of laser wavelengths corresponding to currently available high power lasers. These wavelength pairs were found to be in the range of 585-588 nm and 623-629 for one laser and 1064-1080 nm for the other.
State-insensitive dipole trapping of multilevel atoms can be achieved by an appropriate choice of the wavelength of the trapping laser, so that the interaction with the different transitions results in equal AC Stark shifts for the ground and excited states of interest. However, this approach is severely limited by the availability of coherent sources at the required wavelength and of appropriate power. This work investigates state-insensitive trapping of caesium atoms for which the required wavelength of 935.6 nm is inconvenient in terms of experimental realization. Bichromatic state-insensitive trapping is proposed to overcome the lack of suitable laser sources. We first consider pairs of laser wavelengths in the ratio 1:2 and 1:3, as obtained via second- and third-harmonic generation. We found that the wavelength combinations 931.8–1863.6 nm and 927.5–2782.5 nm are suitable for state-insensitive trapping of caesium atoms. In addition, we examine bichromatic state-insensitive trapping produced by pairs of laser wavelengths corresponding to currently available high-power lasers. These wavelength pairs were found to be in the range of 585–588 nm and 623–629 for one laser and 1064–1080 nm for the other.
State-insensitive trapping plays a significant role in many cold atom experiments. In this technique, trapping at a specific "magic" wavelength leads to identical shifts of the ground and excited states of a particular transition. Hence, the internal state of the trapped atoms remains essentially unaffected by the trapping light. This leads to increased coherence times and loading efficiency, and allows for the use of free-space manipulation techniques. However, the applicability of state-insensitive trapping is limited in terms of light sources available, with restrictions coming from either the required frequency or power. In this thesis, state-insensitive trapping of caesium atoms is considered. It can be achieved at the wavelength of 935.6 nm. However, the present work shows that this wavelength is impractical for experimental realizations of atom trapping in free space due to lack of laser sources with sufficiently high power. We therefore propose bichromatic trapping, as produced by two independent laser fields with different frequencies, to overcome the limitations related to monochromatic trapping. We show that bichromatic trapping extends the range of possible magic wavelengths compared to the specific magic wavelength associated with monochromatic trapping. Specifically, we present results for the magic wavelength combinations for caesium atoms with particular attention to the frequency range of currently available laser sources. Simultaneous state-independent trapping of atomic mixtures of caesium with rubidium and lithium atoms was also investigated, and appropriate magic wavelength combinations were identified. Additionally, species-selective state-independent trapping of atomic mixtures of caesium and lithium was explored and common wavelength pairs for tune-out and magic wavelengths of these atoms were determined.
We study the cancellation of differential ac Stark shifts in the 5s5s5s and 5p5p5p states of the rubidium atom using the linearly and circularly polarized lights by calculating their dynamic polarizabilities. Matrix elements were calculated using a relativistic coupled-cluster method at the single and double excitations and at the important valence triple excitation approximation including all possible nonlinear correlation terms. Some of the important matrix elements were further optimized using the experimental results available for the lifetimes and static polarizabilities of atomic states. ``Magic wavelengths'' are determined from the differential Stark shifts and results for the linearly polarized light are compared with the previously available results. The possible scope of facilitating state-insensitive optical trapping schemes using the magic wavelengths for circularly polarized light is discussed. Using the optimized matrix elements, the lifetimes of the 4d4d4d and 6s6s6s states of this atom are ameliorated.
Magic wavelength optical-dipole trap (ODT) allows confinement of neutral atoms and cancellation of the position-dependent spatially inhomogeneous differential light shift for a desired atomic transition. The light shift of the 87 Rb 5P3/2 state can be expediently tailored to be equal to that of the 87 Rb 5S1/2 state by employing dicromatic (λ1 + λ2 (here λ2 = 2λ1 ∼ 1.5 μm)) linearly polarized ODT lasers. In our calculation, two sets of state-insensitive dichromatic (784.3 + 1568.6 nm and 806.4 + 1612.8 nm) are obtained for the 87 Rb 5S1/2 (F = 2) – 5P3/2 (F � = 3) transition. Further, 784.3 + 1568.6 nm dicromatic laser system with a moderate output power has been realized experimentally by marrying efficient second-harmonic generation using a PPMgO:LN bulk crystal with a fibre-amplified 1.5 μm telecom laser.
Selection of state-insensitive or ``magic'' trapping conditions with ultracold atoms or molecules, where pairs of internal states experience identical trapping potentials, brings substantial benefits to precision measurements and quantum computing schemes. Working at such conditions could ensure that the detrimental effects of inevitable inhomogeneities across an ultracold sample are significantly reduced. However, this aspect of confinement remains unexplored for ultracold polar molecules. Here, we present means to control the ac Stark shift of rotational states of ultracold diatomic polar molecules, when subjected to both trapping laser light and an external electric field. We show that both the strength and relative orientation of the two fields influence the trapping potential. In particular, we predict ``magic electric field strengths'' and a ``magic angle,'' where the Stark shift is independent of the dc external field for certain rotational states of the molecule.