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arXiv:quant-ph/9801023 · Physical Review A

Quantum-state control in optical lattices

Ivan Deutsch, Poul Jessen

Published Mar 1, 1998• 243 citations
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Abstract

We study the means of preparing and coherently manipulating atomic wave packets in optical lattices, with particular emphasis on alkali-metal atoms in the far-detuned limit. We derive a general, basis-independent expression for the lattice potential operator, and show that its off-diagonal elements can be tailored to couple the vibrational manifolds of separate magnetic sublevels. Using these couplings one can evolve the state of a trapped atom in a quantum coherent fashion, and prepare pure quantum states by resolved-sideband Raman cooling. We explore the use of atoms bound in optical lattices to study quantum tunneling and the generation of macroscopic superposition states in a double-well potential. Far-off-resonance optical potentials lend themselves particularly well to reservoir engineering via well-controlled fluctuations in the potential, making the atom-lattice system attractive for the study of decoherence and the connection between classical and quantum physics.

DOI
10.1103/physreva.57.1972

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This dissertation reports on the experimental study of coherent wavepacket dynamics of cesium atoms in the double-well potentials of a one-dimensional, far-off-resonance optical lattice. An optical lattice is the periodic potential produced by the light shift interaction of an atom with the light field of interfering laser beams. With the proper choice of laser parameters and external magnetic fields, an array of double-well potentials is created. Using the techniques of laser cooling, atoms are trapped in the lattice and are prepared in a pure state through a combination of enhanced laser cooling in a near-resonance lattice and state selection in an accelerated far-off-resonance lattice. The atoms are prepared on one side of the double-well potential, and the atomic wavepackets will then oscillate between the left and right localized states of the double-well potential. Entanglement between the internal and external degrees of freedom makes it possible to follow the center-of-mass motion of the atoms by measuring the ground state magnetic populations via Stern-Gerlach analysis. The coherent dynamics of these wavepackets was studied under various combinations of lattice parameters such as lattice depth, applied transverse and longitudinal magnetic fields. There is excellent agreement between the experimentally measured oscillation frequencies and those predicted from a numerical analysis of the bandstructure of the lattice. For certain lattice parameters the total energy of the atom is below the potential barrier and the coherent motion corresponds to tunneling through a classically forbidden barrier. At specific times during the oscillation the atomic wavepacket corresponds to a coherent superposition of the mesoscopically distinct left and right localized states.

•Jan 1, 2000•1 citation
We study the means of preparing and coherently manipulating atomic wave packets in optical lattices, with particular emphasis on alkali-metal atoms in the far-detuned limit. We derive a general, basis-independent expression for the lattice potential operator, and show that its off-diagonal elements can be tailored to couple the vibrational manifolds of separate magnetic sublevels. Using these couplings one can evolve the state of a trapped atom in a quantum coherent fashion, and prepare pure quantum states by resolved-sideband Raman cooling. We explore the use of atoms bound in optical lattices to study quantum tunneling and the generation of macroscopic superposition states in a double-well potential. Far-off-resonance optical potentials lend themselves particularly well to reservoir engineering via well-controlled fluctuations in the potential, making the atom-lattice system attractive for the study of decoherence and the connection between classical and quantum physics.
Optical lattices induced by light detuned far from the frequency of any atomic resonance transition are ideal systems in which to develop techniques for the coherent control of atomic motional and internal states. Decoherence arising from spontaneous emission can be eliminated to an arbitrary degree by varying the detuning of the optical field. The atoms trapped in these lattices are to a large extent isolated from environmental disturbances and from each other. The first step towards the coherent control of atoms in a far-detuned lattice is their preparation in a single motional state. In this thesis the preparation of atoms in the ground vibrational state of a two-dimensional far-detuned optical lattice via resolved-sideband Raman cooling is presented. This sideband-cooling scheme involves stimulated Raman transitions between bound vibrational states of a pair of magnetic ground state sublevels, followed by an irreversible step due to optical pumping, resulting in a net loss of one quantum of vibrational energy per cooling cycle. This process provides efficient cooling in two-dimensions and leads to the accumulation of a large fraction of atoms in the 2-D ground vibrational state of a potential well associated with a single Zeeman substate. Experiments aimed at improving and monitoring the characteristics of the lar-detuned lattice and the sideband-Raman cooling efficiency are also described. Parametric excitation experiments and modelling are employed to investigate the degree of anharmonicity of the optical potential and the importance of heating induced by laser intensity noise, whilst Zeeman-state analysis of the sample is performed for monitoring the distribution of atoms over different magnetic sub- states. Finally, spin-polarization experiments are carried out in order to study the paramagnetic properties of the lattice and lead to an evaluation of a spin-temperature for the sample.
This dissertation reports on quantum state preparation of cesium atoms in a two-dimensional optical lattice, by resolved-sideband Raman cooling. An optical lattice is a periodic potential produced by the light shift interaction between an atom and light field. Laser cooled atoms can become strongly localized about the bottom of potential wells in an optical lattice, where they occupy a discrete spectrum of bound vibrational energy levels. The distribution over vibrational levels of atoms in the lattice is characterized by the mean vibrational excitation, n . In an optical lattice, absorption and emission of photons from lattice beams causes n to increase in time. This source of heating is always present, but its rate can be greatly reduced in a lattice detuned far from the atomic resonance. Sideband cooling is an efficient means of transferring atoms from higher into lower-lying vibrational levels and, thus, it reduces n for the ensemble. If the sideband cooling rate is much greater than the heating rate, then n approaches zero and virtually all atoms are in the lowest vibrational level in their potential wells. Our sideband cooling scheme involves stimulated Raman transitions between bound states in the potential wells of a pair of magnetic sublevels, followed by optical pumping, for a net loss of one quantum of vibration per cooling cycle. The process accumulates 98% of atoms in the ground vibrational level of a potential well associated with a single Zeeman substate. Each atom in the lattice is then very close to a pure state. For two-dimensional lattice with sideband cooling we find nx≈ny≈0.008 &parl0;16&parr0; . Various issues related to state preparation and sideband cooling are also discussed in the context of a one dimensional lin ⊥ lin optical lattice. These include improvement of laser cooling in a near resonance lattice by application of weak magnetic fields, transfer of atoms from near into far off-resonance lattices, and heating rates in far off-resonance lattices.
Summary form only given. The AC-Stark shift of a set of interfering laser beams together with the Zeeman interaction with external magnetic fields provide flexible mechanisms for coherently controlling atomic wave packets. When detuned far from atomic resonance, these optical lattices can trap cold atoms with minimal dissipation and thus provide an ideal environment for observing quantum coherent phenomena. We consider a one dimensional lattice of double wells produced by counterpropagating linearly polarized laser beams and a static magnetic field transverse to the laser wave vectors.
We trap neutral Cs atoms in a two-dimensional optical lattice and cool them close to the zero point of motion by resolved-sideband Raman cooling. Sideband cooling occurs via transitions between the vibrational manifolds associated with a pair of magnetic sublevels, and the required Raman coupling is provided by the lattice potential itself. We obtain mean vibrational excitations ${\overline{n}}_{x}\ensuremath{\approx}{\overline{n}}_{y}<0.024$, corresponding to a population >95>95%>95 in the vibrational ground state. Atoms in the ground state of an optical lattice provide a new system in which to explore quantum state control and subrecoil laser cooling.
We form a 1D optical lattices for Cs atoms using light tuned a few thousand linewidths below the 6S1/2(F equals 4) yields 6P3/2(F' equals 5) transition at 852 nm. In this far-off- resonance lattice the time scale for damping of motional coherences and kinetic energy can be orders of magnitude longer than the vibrational oscillation period for atoms trapped in the lattice potential wells. Atoms are loaded directly into deeply bound states, by adiabatic transfer from a superimposed, near-resonance optical lattice. This yields a mean vibrational excitation n approximately equals 0.3, and localization (Delta) z approximately (lambda) /20 deep in the Lamb-Dicke regime. Light scattering subsequently heats the atoms, but the initial rate is only of order 10-3 vibrational quanta per oscillation period. Low vibrational excitation, localization in the Lamb-Dicke regime and low heating rates make these atoms good candidates for resolved- sideband Raman cooling, and for the generation and study of non-classical states of center-of-mass motion. We propose a scheme for resolved-sideband Raman cooling and quantum state preparation; the scheme employs Raman coupling between magnetic sublevels induced by the lattice light field itself.
This dissertation reports on the experimental study of coherent wavepacket dynamics of cesium atoms in the double-well potentials of a one-dimensional, far-off-resonance optical lattice. An optical lattice is the periodic potential produced by the light shift interaction of an atom with the light field of interfering laser beams. With the proper choice of laser parameters and external magnetic fields, an array of double-well potentials is created. Using the techniques of laser cooling, atoms are trapped in the lattice and are prepared in a pure state through a combination of enhanced laser cooling in a near-resonance lattice and state selection in an accelerated far-off-resonance lattice. The atoms are prepared on one side of the double-well potential, and the atomic wavepackets will then oscillate between the left and right localized states of the double-well potential. Entanglement between the internal and external degrees of freedom makes it possible to follow the center-of-mass motion of the atoms by measuring the ground state magnetic populations via Stern-Gerlach analysis. The coherent dynamics of these wavepackets was studied under various combinations of lattice parameters such as lattice depth, applied transverse and longitudinal magnetic fields. There is excellent agreement between the experimentally measured oscillation frequencies and those predicted from a numerical analysis of the bandstructure of the lattice. For certain lattice parameters the total energy of the atom is below the potential barrier and the coherent motion corresponds to tunneling through a classically forbidden barrier. At specific times during the oscillation the atomic wavepacket corresponds to a coherent superposition of the mesoscopically distinct left and right localized states.