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Sub-wavelength resonance imaging and addressing of cesium atoms trapped in an optical lattice

Jae Hoon Lee

Published Jan 1, 2012• 2 citations
OpenAlex

Abstract

We demonstrate a resonance imaging protocol for optical lattices that enables robust preparation and single qubit addressing of atoms with sub-wavelength resolution in 1D. A 3D optical lattice consisting of three sets of independent 1D counter- propagating laser beams provides the trapping potential for the atoms. On this optical lattice platform, a long-period 1D superlattice is imposed by interfering two laser beams at a shallow angle centered at the atoms. This superlattice creates a position-dependent shift of the qubit transition frequency defined between two spin states in the ground manifold. Isolated 2D planes of atoms are prepared by flipping the resonant spins with a microwave pulse and removing the non-resonant spins by pushing them out of the lattice with a resonant laser beam. The periodic planes of atoms that are prepared can be imaged by applying another microwave pulse and detecting the fluorescence from the spins that flip back to the initial state, as a function of superlattice displacement between the preparation and read-out pulses. By employing these new techniques for sub-wavelength imaging, we tested the effectiveness of using composite pulses for addressing the trapped atoms in an optical lattice. Composite pulse techniques can be used to reduce the sensitivity of the addressing to small variations in the relative position and intensity of the lattices. This robustness is achieved by applying numerically generated composite pulses that have a constant atomic response within a target range of relative lattice positions and intensities. We designed a composite microwave pulse that flips the spin with near unit fidelity for all atoms that are positioned within a target spatial region, while conserving the spin of the atoms outside of that region. This cannot be accomplished with plain pulses due to off-resonant excitation. We also expanded the concept of this technique for robustly addressing spins even further to implement independent unitaries, or single qubit quantum gates, across several adjacent lattice sites. Finally, in order to quantitatively measure the fidelity of these robust composite pulses, we perform a randomized benchmarking procedure, which was first proposed by Knill.

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We study a system of neutral atoms trapped in a three-dimensional optical lattice suitable for the encoding, initialization and manipulation of atomic qubits. The qubits are manipulated by applied electromagnetic fields interacting with dipole moments of the atoms via light shifts, Raman transitions, Zeeman shifts, and microwave transitions. Our lattice is formed by three orthogonal one-dimensional lattices, which have different frequencies so that interference terms average to zero. This geometry allows considerable freedom in designing the component one-dimensional lattices, so that they provide not only confinement but also independent control in each dimension. Our atomic qubits are initialized from a laser-cooled atomic sample by Raman sideband cooling in individual lattice potential wells. We have demonstrated accurate and robust one-qubit manipulation using resonant microwave fields. In practice such control operations are always subject to errors, in our case spatial inhomogeneities in the microwave Rabi frequency and the light shifted qubit transition frequency. Observation of qubit dynamics in near real time allows us to minimize these inhomogeneities, and therefore optimize qubit logic gates. For qubits in the lattice, we infer a fidelity of 0.990(3) for a single pi-pulse. We have also explored the use of NMR-type pulse techniques in order to further reduce the effect of errors and thus improve gate robustness in the atom/lattice system. Our schemes for two-qubit quantum logic operations are based on controlled collisional interactions. We have experimented with two schemes in order to probe these collisions. The first involves manipulation of the center-of-mass wavepackets of two qubits in a geometry corresponding to two partially overlapping Mach-Zender interferometers. Unfortunately, this scheme has proven extremely sensitive to phase errors, as the wavepackets are moved by the optical lattice. The other scheme starts with two qubits in spatially separated traps, and utilizes microwaves to drive one or both qubits into a third trap in-between the two qubits. Once the wavepackets overlap, the collisions create a large energy shift which can be probed spectroscopically.

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Microwave control of atomic motion in a spin dependent optical lattice

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The subject of this work is the control of the quantum mechanical motional state of trapped neutral Cesium atoms. This is accomplished using a rarely considered method based on microwave radiation in combination with a spin dependent optical lattice potential. The setup used was designed to trap and to store on the order of ten atoms in a one dimensional optical lattice. Fluorescence imaging allows to determine both, the number and the position of the atoms. The spin degree of freedom is manipulated using microwave radiation and the trapping potential allows to shift the atoms to the 'left' or to the 'right' along the potential axis, depending on their spin orientation. A microwave spectrum with a slightly displaced lattice exhibits sideband peaks corresponding to a change of the vibrational quantum number. This is the mechanism which introduces coupling between the spin and the motional degree of freedom. The work draws parallels to the usually used sideband technique based on optical transitions instead of microwaves and exploiting the photon recoil instead of a state dependent potential. Similar to the optical method the microwave based approach allows for the realization of a resolved-sideband cooling technique which efficiently prepares the atomic ensemble in the motional ground state. Starting from this purified quantum mechanical state, other interesting states are prepared using successive sideband transitions. The result of the preparation is probed by implementing filtering schemes for the motional state. With this control technique the experimental setup in total is capable to control the spin, the position along the one dimensional periodic potential and the vibrational state of the atoms.

•Oct 15, 2010•4 citations

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Abstract Imaging is central to gaining microscopic insight into physical systems, and new microscopy methods have always led to the discovery of new phenomena and a deeper understanding of them. Ultracold atoms in optical lattices provide a quantum simulation platform, featuring a variety of advanced detection tools including direct optical imaging while pinning the atoms in the lattice1,2. However, this approach suffers from the diffraction limit, high optical density and small depth of focus, limiting it to two-dimensional (2D) systems. Here we introduce an imaging approach where matter wave optics magnifies the density distribution before optical imaging, allowing 2D sub-lattice-spacing resolution in three-dimensional (3D) systems. By combining the site-resolved imaging with magnetic resonance techniques for local addressing of individual lattice sites, we demonstrate full accessibility to 2D local information and manipulation in 3D systems. We employ the high-resolution images for precision thermodynamics of Bose–Einstein condensates in optical lattices as well as studies of thermalization dynamics driven by thermal hopping. The sub-lattice resolution is demonstrated via quench dynamics within the lattice sites. The method opens the path for spatially resolved studies of new quantum many-body regimes, including exotic lattice geometries or sub-wavelength lattices3–6, and paves the way for single-atom-resolved imaging of atomic species, where efficient laser cooling or deep optical traps are not available, but which substantially enrich the toolbox of quantum simulation of many-body systems.

arXiv:2104.10089•Nature•Nov 24, 2021•46 citations

Towards an imaging lattice for magnetically trapped atoms

E. Owen

The imaging of neutral atoms confined in an optical lattice has been demonstrated by a number of groups, resolving single fluorescing atoms in samples of hundreds of atoms. To obtain a high signal the atoms remain confined in the wells of a deep optical lattice whilst fluorescence excitation light is applied for high resolution imaging. In most cases, the excitation light frequency is chosen so that there is a concomitant laser cooling effect. In existing implementations of an imaging lattice the preceding manipulation stage has used optical trapping and manipulation. In this thesis I describe work towards applying this imaging lattice technique on a magnetic trapping apparatus, in particular for carrying out quantum simulation experiments. An introduction to the specific challenge of performing a quantum simulation of the fractional quantum Hall effect is given, with the link to and nature of the imaging lattice technique explained. The existing quantum-gas machine that has been developed to produce Bose-Einstein condensates of 87Rb in this work is then described, including the new optical lattice subsystem and the associated diode laser system. An auxiliary project to develop a servo-control system for frequencies that are several GHz away from an atomic reference is presented. We implement an optical lattice using laser light with a frequency detuning of -20 GHz below the D1-resonance line. The construction and geometry of the individual dipole trapping beams in combination with our existing apparatus is discussed as well as the alignment methods used. We confirm the presence of three independent 1D lattices through diffraction, and observe the decay of a BEC loaded into a lattice using absorption imaging. We observe good long-term alignment and operational stability of the optical lattice. This system will enable us to ultimately detect single fluorescing atoms in the optical lattice, following the application of excitation light co-propogating with lattice beams, via an imaging system with a moderate numerical aperture of 0:27.

•Jan 1, 2017•0 citations

Single-Atom Resolved Imaging and Manipulation in an Atomic Mott Insulator

Christof Weitenberg

This thesis reports on new experimental techniques for the study of strongly correlated states of ultracold atoms in optical lattices. We used a high numerical aperture imaging system to probe 87Rb atoms in a two-dimensional lattice with single-site resolution. Fluorescence imaging allows to detect single atoms with a large signal to noise ratio and to reconstruct the atom distribution on the lattice. We applied this new technique to a two-dimensional Mott insulator and directly observed number squeezing and the emerging shell structure. A comparison of the radial density and variance distributions to theory provides a precise in situ temperature and entropy measurement from single images. We find entropies around the critical value for quantum magnetism. In a second series of experiments, we demonstrated two-dimensional single-site spin control in the optical lattice. The differential light shift of a tightly focused laser beam shifts selected atoms into resonance with a microwave field driving a spin flip. In this way, we reach sub-diffraction limited spatial resolution well below the lattice spacing. Starting from a Mott insulator with unity filling we were able to create arbitrary spin patterns. We used this ability to prepare atom distributions to study one-dimensional single-particle tunneling dynamics in a lattice. By discriminating the dynamics of the ground state and of the first excited band, we find that our addressing scheme leaves most atoms in the vibrational ground state. Moreover, we studied coherent light scattering from the atoms in the optical lattice and found diffraction maxima in the far-field. We showed that an antiferromagnetic order leads to additional diffraction peaks which can be used to detect this order also when single-site resolution is not available. The new techniques described in this thesis open the path to a wide range of novel applications from quantum dynamics of spin impurities, entropy transport, implementation of novel cooling schemes, and engineering of quantum many-body phases to quantum information processing.

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Single-site addressing of ultracold atoms beyond the diffraction limit via position-dependent adiabatic passage

Daniel Viscor, J. L. Rubio, G. Birkl +2 more

We propose a single-site addressing implementation based on the subwavelength localization via adiabatic passage (SLAP) technique. We consider a sample of ultracold neutral atoms loaded into a two-dimensional optical lattice with one atom per site. Each atom is modeled by a three-level $\ensuremath{\Lambda}$ system in interaction with a pump and a Stokes laser pulse. Using a pump field with a node in its spatial profile, the atoms at all sites are transferred from one ground state of the system to the other via stimulated Raman adiabatic passage, except the one at the position of the node that remains in the initial ground state. This technique allows for the preparation, manipulation, and detection of atoms with a spatial resolution better than the diffraction limit, which either relaxes the requirements on the optical setup used or extends the achievable spatial resolution to lattice spacings smaller than accessible to date. In comparison to techniques based on coherent population trapping, SLAP gives a higher addressing resolution and has additional advantages such as robustness against parameter variations, coherence of the transfer process, and the absence of photon induced recoil. Additionally, the advantages of our proposal with respect to adiabatic spin-flip techniques are highlighted. Analytic expressions for the achievable addressing resolution and efficiency are derived and compared to numerical simulations for ${}^{87}$Rb atoms in state-of-the-art optical lattices.

arXiv:1301.1546•Physical Review A•Dec 17, 2012•14 citations
We demonstrate a resonance imaging protocol for optical lattices that enables robust preparation and single qubit addressing of atoms with sub-wavelength resolution in 1D. A 3D optical lattice consisting of three sets of independent 1D counter- propagating laser beams provides the trapping potential for the atoms. On this optical lattice platform, a long-period 1D superlattice is imposed by interfering two laser beams at a shallow angle centered at the atoms. This superlattice creates a position-dependent shift of the qubit transition frequency defined between two spin states in the ground manifold. Isolated 2D planes of atoms are prepared by flipping the resonant spins with a microwave pulse and removing the non-resonant spins by pushing them out of the lattice with a resonant laser beam. The periodic planes of atoms that are prepared can be imaged by applying another microwave pulse and detecting the fluorescence from the spins that flip back to the initial state, as a function of superlattice displacement between the preparation and read-out pulses. By employing these new techniques for sub-wavelength imaging, we tested the effectiveness of using composite pulses for addressing the trapped atoms in an optical lattice. Composite pulse techniques can be used to reduce the sensitivity of the addressing to small variations in the relative position and intensity of the lattices. This robustness is achieved by applying numerically generated composite pulses that have a constant atomic response within a target range of relative lattice positions and intensities. We designed a composite microwave pulse that flips the spin with near unit fidelity for all atoms that are positioned within a target spatial region, while conserving the spin of the atoms outside of that region. This cannot be accomplished with plain pulses due to off-resonant excitation. We also expanded the concept of this technique for robustly addressing spins even further to implement independent unitaries, or single qubit quantum gates, across several adjacent lattice sites. Finally, in order to quantitatively measure the fidelity of these robust composite pulses, we perform a randomized benchmarking procedure, which was first proposed by Knill.
We study a system of neutral atoms trapped in a three-dimensional optical lattice suitable for the encoding, initialization and manipulation of atomic qubits. The qubits are manipulated by applied electromagnetic fields interacting with dipole moments of the atoms via light shifts, Raman transitions, Zeeman shifts, and microwave transitions. Our lattice is formed by three orthogonal one-dimensional lattices, which have different frequencies so that interference terms average to zero. This geometry allows considerable freedom in designing the component one-dimensional lattices, so that they provide not only confinement but also independent control in each dimension. Our atomic qubits are initialized from a laser-cooled atomic sample by Raman sideband cooling in individual lattice potential wells. We have demonstrated accurate and robust one-qubit manipulation using resonant microwave fields. In practice such control operations are always subject to errors, in our case spatial inhomogeneities in the microwave Rabi frequency and the light shifted qubit transition frequency. Observation of qubit dynamics in near real time allows us to minimize these inhomogeneities, and therefore optimize qubit logic gates. For qubits in the lattice, we infer a fidelity of 0.990(3) for a single pi-pulse. We have also explored the use of NMR-type pulse techniques in order to further reduce the effect of errors and thus improve gate robustness in the atom/lattice system. Our schemes for two-qubit quantum logic operations are based on controlled collisional interactions. We have experimented with two schemes in order to probe these collisions. The first involves manipulation of the center-of-mass wavepackets of two qubits in a geometry corresponding to two partially overlapping Mach-Zender interferometers. Unfortunately, this scheme has proven extremely sensitive to phase errors, as the wavepackets are moved by the optical lattice. The other scheme starts with two qubits in spatially separated traps, and utilizes microwaves to drive one or both qubits into a third trap in-between the two qubits. Once the wavepackets overlap, the collisions create a large energy shift which can be probed spectroscopically.
The subject of this work is the control of the quantum mechanical motional state of trapped neutral Cesium atoms. This is accomplished using a rarely considered method based on microwave radiation in combination with a spin dependent optical lattice potential. The setup used was designed to trap and to store on the order of ten atoms in a one dimensional optical lattice. Fluorescence imaging allows to determine both, the number and the position of the atoms. The spin degree of freedom is manipulated using microwave radiation and the trapping potential allows to shift the atoms to the 'left' or to the 'right' along the potential axis, depending on their spin orientation. A microwave spectrum with a slightly displaced lattice exhibits sideband peaks corresponding to a change of the vibrational quantum number. This is the mechanism which introduces coupling between the spin and the motional degree of freedom. The work draws parallels to the usually used sideband technique based on optical transitions instead of microwaves and exploiting the photon recoil instead of a state dependent potential. Similar to the optical method the microwave based approach allows for the realization of a resolved-sideband cooling technique which efficiently prepares the atomic ensemble in the motional ground state. Starting from this purified quantum mechanical state, other interesting states are prepared using successive sideband transitions. The result of the preparation is probed by implementing filtering schemes for the motional state. With this control technique the experimental setup in total is capable to control the spin, the position along the one dimensional periodic potential and the vibrational state of the atoms.
Abstract Imaging is central to gaining microscopic insight into physical systems, and new microscopy methods have always led to the discovery of new phenomena and a deeper understanding of them. Ultracold atoms in optical lattices provide a quantum simulation platform, featuring a variety of advanced detection tools including direct optical imaging while pinning the atoms in the lattice1,2. However, this approach suffers from the diffraction limit, high optical density and small depth of focus, limiting it to two-dimensional (2D) systems. Here we introduce an imaging approach where matter wave optics magnifies the density distribution before optical imaging, allowing 2D sub-lattice-spacing resolution in three-dimensional (3D) systems. By combining the site-resolved imaging with magnetic resonance techniques for local addressing of individual lattice sites, we demonstrate full accessibility to 2D local information and manipulation in 3D systems. We employ the high-resolution images for precision thermodynamics of Bose–Einstein condensates in optical lattices as well as studies of thermalization dynamics driven by thermal hopping. The sub-lattice resolution is demonstrated via quench dynamics within the lattice sites. The method opens the path for spatially resolved studies of new quantum many-body regimes, including exotic lattice geometries or sub-wavelength lattices3–6, and paves the way for single-atom-resolved imaging of atomic species, where efficient laser cooling or deep optical traps are not available, but which substantially enrich the toolbox of quantum simulation of many-body systems.
The imaging of neutral atoms confined in an optical lattice has been demonstrated by a number of groups, resolving single fluorescing atoms in samples of hundreds of atoms. To obtain a high signal the atoms remain confined in the wells of a deep optical lattice whilst fluorescence excitation light is applied for high resolution imaging. In most cases, the excitation light frequency is chosen so that there is a concomitant laser cooling effect. In existing implementations of an imaging lattice the preceding manipulation stage has used optical trapping and manipulation. In this thesis I describe work towards applying this imaging lattice technique on a magnetic trapping apparatus, in particular for carrying out quantum simulation experiments. An introduction to the specific challenge of performing a quantum simulation of the fractional quantum Hall effect is given, with the link to and nature of the imaging lattice technique explained. The existing quantum-gas machine that has been developed to produce Bose-Einstein condensates of 87Rb in this work is then described, including the new optical lattice subsystem and the associated diode laser system. An auxiliary project to develop a servo-control system for frequencies that are several GHz away from an atomic reference is presented. We implement an optical lattice using laser light with a frequency detuning of -20 GHz below the D1-resonance line. The construction and geometry of the individual dipole trapping beams in combination with our existing apparatus is discussed as well as the alignment methods used. We confirm the presence of three independent 1D lattices through diffraction, and observe the decay of a BEC loaded into a lattice using absorption imaging. We observe good long-term alignment and operational stability of the optical lattice. This system will enable us to ultimately detect single fluorescing atoms in the optical lattice, following the application of excitation light co-propogating with lattice beams, via an imaging system with a moderate numerical aperture of 0:27.
This thesis reports on new experimental techniques for the study of strongly correlated states of ultracold atoms in optical lattices. We used a high numerical aperture imaging system to probe 87Rb atoms in a two-dimensional lattice with single-site resolution. Fluorescence imaging allows to detect single atoms with a large signal to noise ratio and to reconstruct the atom distribution on the lattice. We applied this new technique to a two-dimensional Mott insulator and directly observed number squeezing and the emerging shell structure. A comparison of the radial density and variance distributions to theory provides a precise in situ temperature and entropy measurement from single images. We find entropies around the critical value for quantum magnetism. In a second series of experiments, we demonstrated two-dimensional single-site spin control in the optical lattice. The differential light shift of a tightly focused laser beam shifts selected atoms into resonance with a microwave field driving a spin flip. In this way, we reach sub-diffraction limited spatial resolution well below the lattice spacing. Starting from a Mott insulator with unity filling we were able to create arbitrary spin patterns. We used this ability to prepare atom distributions to study one-dimensional single-particle tunneling dynamics in a lattice. By discriminating the dynamics of the ground state and of the first excited band, we find that our addressing scheme leaves most atoms in the vibrational ground state. Moreover, we studied coherent light scattering from the atoms in the optical lattice and found diffraction maxima in the far-field. We showed that an antiferromagnetic order leads to additional diffraction peaks which can be used to detect this order also when single-site resolution is not available. The new techniques described in this thesis open the path to a wide range of novel applications from quantum dynamics of spin impurities, entropy transport, implementation of novel cooling schemes, and engineering of quantum many-body phases to quantum information processing.
We propose a single-site addressing implementation based on the subwavelength localization via adiabatic passage (SLAP) technique. We consider a sample of ultracold neutral atoms loaded into a two-dimensional optical lattice with one atom per site. Each atom is modeled by a three-level $\ensuremath{\Lambda}$ system in interaction with a pump and a Stokes laser pulse. Using a pump field with a node in its spatial profile, the atoms at all sites are transferred from one ground state of the system to the other via stimulated Raman adiabatic passage, except the one at the position of the node that remains in the initial ground state. This technique allows for the preparation, manipulation, and detection of atoms with a spatial resolution better than the diffraction limit, which either relaxes the requirements on the optical setup used or extends the achievable spatial resolution to lattice spacings smaller than accessible to date. In comparison to techniques based on coherent population trapping, SLAP gives a higher addressing resolution and has additional advantages such as robustness against parameter variations, coherence of the transfer process, and the absence of photon induced recoil. Additionally, the advantages of our proposal with respect to adiabatic spin-flip techniques are highlighted. Analytic expressions for the achievable addressing resolution and efficiency are derived and compared to numerical simulations for 87{}^{87}87Rb atoms in state-of-the-art optical lattices.