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Quantum Control of Vibrational States in an Optical Lattice

Chao Zhuang

Published Jan 14, 2014• 0 citations
OpenAlex

Abstract

In this thesis, I present an experimental study of quantum control techniques for transferring population between vibrational states of atoms trapped in an optical lattice. Results from a range of techniques are compared, including techniques tested previously in the same system. In the study of the Adiabatic Rapid Passage (ARP) technique, control of population transfer is realized through varying the chirp rate and modulation amplitude of a frequency-chirped sinusoidal displacement of the lattice. Meanwhile, dependence of population transfer on the chirp direction is observed, which is explained by a model of ARP in a 3-level system. In the study of the coherent control technique, interference between a one-phonon transition at 2\omega and a two-phonon transition at omega is experimentally demonstrated. The omega and 2\omega transitions are realized by sinusoidally displacing the optical lattice at omega and sinusoidally modulating the lattice depth at 2\omega, respectively. The branching ratio of transitions to the first excited state and to higher excited states is controlled by varying the relative phase between these two pathways. The highest measured branching ratio of 17\pm2 is achieved among all the experiments using this coherent control scheme. In the study of the GRadient Ascent Pulse Engineering (GRAPE) technique, a "pulse" involving both displacement and depth-modulation of the lattice is used to transfer population. This pulse is theoretically engineered with the GRAPE algorithm to optimize the fidelity between the first excited state and the final state, when the lattice Hamiltonian without gravity for a specific lattice depth is considered. The experimental result shows that there is almost no excitation into higher excited states during population transfer from the ground to the first excited state, even when this process is affected by gravity and inhomogeneous broadening in reality. By comparing all the techniques, the GRAPE technique is found to be the best in terms of increasing population transfer into the first excited state while reducing excitation into higher excited states. On the other hand, the ARP technique creates the highest normalized population inversion, a ratio of the difference to the sum of the ground and the first excited state populations.

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Quantum control of population transfer between vibrational states in an optical lattice

Matin Hallaji, Chao Zhuang, Alex Hayat +4 more

We study quantum control techniques, specifically Adiabatic Rapid Passage (ARP) and Gradient Ascent Pulse Engineering (GRAPE), for transferring atoms trapped in an optical lattice between different vibrational states. We compare them with each other and with previously studied coupling schemes in terms of performance. In our study of ARP, we realize control of the vibrational states by tuning the frequency of a spatial modulation through the inhomogeneously broadened vibrational absorption spectrum. We show that due to the presence of multiple crossings, the population transfer depends on the direction of the frequency sweep, in contrast to traditional ARP. In a second study, we control these states by applying a pulse sequence involving both the displacement of the optical lattice and modulation of the lattice depth. This pulse is engineered via the GRAPE algorithm to maximize the number of atoms transferred from the initial (ground) state to the first excited state. We find that the ARP and the GRAPE techniques are superior to the previously tested techniques at transferring population into the first excited state from the ground state: $38.9\pm0.2\%$ and $39\pm2\%$ respectively. GRAPE outperforms ARP in leaving the higher excited states unpopulated (less than $3.3\%$ of the ground state population, at $84\%$ confidence level), while $18.7\pm0.3\%$ of the ground state population is transferred into higher excited states by using ARP. On the other hand, ARP creates a normalized population inversion of $0.21\pm0.02$, which is the highest obtained by any of the control techniques we have investigated.

arXiv:1510.09186•Oct 30, 2015•0 citations

Coherent Control of Population Transfer between Vibrational States in an Optical Lattice via Two-Path Quantum Interference

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We demonstrate coherent control of population transfer between vibrational states in an optical lattice by using interference between a one-phonon transition at 2ω and a two-phonon transition at ω. The ω and 2ω transitions are driven by phase- and amplitude-modulation of the lattice laser beams, respectively. By varying the relative phase of these two pathways, we control the branching ratio between transitions to the first excited state and those to the higher states. Our best result shows a branching ratio of 17±2, which is the highest among coherent control experiments using analogous schemes. Such quantum control techniques may find broad application in suppressing leakage errors in a variety of quantum information architectures.

arXiv:1207.6427•Physical Review Letters•Dec 3, 2013•22 citations

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We investigate methods related to achieving interaction between photonic qubits. The first general approach to achieve this is to transfer photonic qubits to solid state systems, where the qubit interactions can then take place. The other approach is to enhance the strength of the photon-photon interaction. -- We first robustly study methods related to the first approach: in particular we focus on how to convert the photonic quantised excitation into an atomic excitation. The Stark-shift-chirped rapid adiabatic passage (SCRAP) technique in a three level Λ-type system is a coherent population transfer (CPT) technique similar to Stimulated Raman Adiabatic Passage (STIRAP), which in itself is closely related to electro-magnetically induced transparency (EIT). SCRAP has been shown to perform CPT with a high delity for a range of different detunings making SCRAP far more robust when there is large inhomogeneous broadenings present in the ensemble. We make use of optimum control techniques in order to optimise the standard SCRAP pulses so as to minimise the decrease in delity brought on by inhomogeneous broadenings of the transitions. Our result is that we can improve the average delity of population transfer over a wide range of detunings for both the ground to excited state detuning and the ground to target state detuning (two-photon detuning). -- Finally we consider the enhancement of photon-photon interactions and the implementation of an optical quantum controlled not (CNOT) gate via a cavity-QED setup. We explore the Nitrogen-vacancy centre in diamond as a suitable four-level tripod system in which to generate the cross-Kerr nonlinearity required to facilitate the strong interaction between the two fields (control and target) held in a cavity. We show that with an ultra-high quality factor cavity, and only a single NV centre strongly coupled to the trapped light, a suffciently large interaction can be generated between the two fields to obtain a conditional phase shift (CPS) in excess of the required π for the successful implementation of a CNOT gate. We also show that it is possible to use this system to create an entangled state of two macroscopically distinguishable states, that is a Schrödinger cat state, by using two weak coherent fields as input and making a measurement on the second field.

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In this thesis, I report on experiments with cold 85Rb atoms in a far-detuned one-dimensional optical lattice. These experiments are focused on creating efficient coupling between the quantized vibrational states of atoms in the optical lattice, on controlling and maintaining coherence between the vibrational states, and on developing a spectroscopy method to characterize the decay of coherence. First, I present an experimental study of the application of simple and compound pulses consisting of time-dependent spatial translations to coupling vibrational states of ultracold 85Rb atoms in the optical\nlattice. Experimental results show that a square pulse consisting of lattice displacements and a delay is more efficient than single-step and Gaussian pulses. The square pulse can be seen as an example of coherent control. Numerical calculations are in strong agreement with the experimental results. In addition, it is shown numerically that the vibrational state coupling due to such lattice manipulations is more efficient in shallow lattices than in deep lattices, in which the coupling probability approaches the harmonic\noscillator limit. Next, the effectiveness of these pulses in reviving oscillations of atoms in vibrational superposition states using a pulse-echo technique is examined. Experimental results show that the square and Gaussian pulses result in higher echo amplitudes than the single-step pulse. These echo amplitudes are an order of magnitude larger than the echo amplitudes observed previously for the motional states of atoms in optical lattices.\nWith the aim of the optimized square echo pulse, echo amplitude is measured at much\nlonger times, where a surprising coherence freeze (plateau) is observed. To investigate \nmechanisms responsible for the observed echo decay and the coherence freeze, we developed\na new two-dimensional pump-probe spectroscopy technique to monitor the evolution of frequency-frequency correlations in the system, a necessary input for understanding the decay of coherence. Through this 2D technique, we have characterized the temporal decay of frequency memory and through our simulations we find that coherence freeze is related to the shape of this memory loss function. This technique is general in that it can be applied in a variety of quantum information candidate systems to probe the nature of their decoherence.

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Abstract Effcient population transfer and motional state control are important for optical lattice clocks and precision experiments with lattice-trapped neutral atoms. Here we experimentally investigate adiabatic rapid passage (ARP) on the clock transition of a one-dimensional 87 Sr optical lattice clock and develop a mode-resolved model for ARP on motional sidebands. On the carrier transition, ARP enables robust internal-state transfer with a maximum excitation fraction of 0.98(2). On the blue motional sideband, ARP increases the maximum excitation fraction from 0.47(2) to 0.55(3), and the measured dynamics are consistently reproduced by the mode-resolved model. The model further predicts that the sideband transfer effciency can exceed 0.88 when the carrier Rabi frequency is increased to 15 kHz. Applying ARP to the red-sideband cooling reduces the axial mean vibrational occupation to approximately 0.038, corresponding to a motional ground-state population of 0.96. These results provide a quantitative basis for designing ARP excitation on motional sidebands and for optimizing sideband cooling in lattice-trapped atoms, with direct relevance to coherent state preparation in optical lattice clocks and related precision-measurement experiments in neutral atoms.

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Quantum Control of Population Transfer and Vibrational States via Chirped Pulses in Four Level Density Matrix Equations

Iduabo John Afa, Carles Serrat

We investigate the effect of chirped excitation and the excitation detuning on the coherent control of population transfer and vibrational states in a four-level system. Density matrix equations are studied for optimally enhanced processes by considering specific parameters typical of oxazine systems. Our simulations show a strong dependence on the interplay between chirp and excitation detuning and predict enhancement factors up to 3.2 for population transfer and up to 38.5 for vibrational coherences of electronic excited states. The study of the dynamics of the populations and vibrational coherences involved in the four-level system allows an interpretation of the different enhancement/suppression processes observed.

Applied Sciences•Nov 15, 2016•5 citations
In this thesis, I present an experimental study of quantum control techniques for transferring population between vibrational states of atoms trapped in an optical lattice. Results from a range of techniques are compared, including techniques tested previously in the same system. In the study of the Adiabatic Rapid Passage (ARP) technique, control of population transfer is realized through varying the chirp rate and modulation amplitude of a frequency-chirped sinusoidal displacement of the lattice. Meanwhile, dependence of population transfer on the chirp direction is observed, which is explained by a model of ARP in a 3-level system. In the study of the coherent control technique, interference between a one-phonon transition at 2\omega and a two-phonon transition at omega is experimentally demonstrated. The omega and 2\omega transitions are realized by sinusoidally displacing the optical lattice at omega and sinusoidally modulating the lattice depth at 2\omega, respectively. The branching ratio of transitions to the first excited state and to higher excited states is controlled by varying the relative phase between these two pathways. The highest measured branching ratio of 17\pm2 is achieved among all the experiments using this coherent control scheme. In the study of the GRadient Ascent Pulse Engineering (GRAPE) technique, a "pulse" involving both displacement and depth-modulation of the lattice is used to transfer population. This pulse is theoretically engineered with the GRAPE algorithm to optimize the fidelity between the first excited state and the final state, when the lattice Hamiltonian without gravity for a specific lattice depth is considered. The experimental result shows that there is almost no excitation into higher excited states during population transfer from the ground to the first excited state, even when this process is affected by gravity and inhomogeneous broadening in reality. By comparing all the techniques, the GRAPE technique is found to be the best in terms of increasing population transfer into the first excited state while reducing excitation into higher excited states. On the other hand, the ARP technique creates the highest normalized population inversion, a ratio of the difference to the sum of the ground and the first excited state populations.
We study quantum control techniques, specifically Adiabatic Rapid Passage (ARP) and Gradient Ascent Pulse Engineering (GRAPE), for transferring atoms trapped in an optical lattice between different vibrational states. We compare them with each other and with previously studied coupling schemes in terms of performance. In our study of ARP, we realize control of the vibrational states by tuning the frequency of a spatial modulation through the inhomogeneously broadened vibrational absorption spectrum. We show that due to the presence of multiple crossings, the population transfer depends on the direction of the frequency sweep, in contrast to traditional ARP. In a second study, we control these states by applying a pulse sequence involving both the displacement of the optical lattice and modulation of the lattice depth. This pulse is engineered via the GRAPE algorithm to maximize the number of atoms transferred from the initial (ground) state to the first excited state. We find that the ARP and the GRAPE techniques are superior to the previously tested techniques at transferring population into the first excited state from the ground state: 38.9±0.2%38.9\pm0.2\%38.9±0.2% and 39±2%39\pm2\%39±2% respectively. GRAPE outperforms ARP in leaving the higher excited states unpopulated (less than 3.3%3.3\%3.3% of the ground state population, at 84%84\%84% confidence level), while 18.7±0.3%18.7\pm0.3\%18.7±0.3% of the ground state population is transferred into higher excited states by using ARP. On the other hand, ARP creates a normalized population inversion of 0.21±0.020.21\pm0.020.21±0.02, which is the highest obtained by any of the control techniques we have investigated.
We demonstrate coherent control of population transfer between vibrational states in an optical lattice by using interference between a one-phonon transition at 2ω and a two-phonon transition at ω. The ω and 2ω transitions are driven by phase- and amplitude-modulation of the lattice laser beams, respectively. By varying the relative phase of these two pathways, we control the branching ratio between transitions to the first excited state and those to the higher states. Our best result shows a branching ratio of 17±2, which is the highest among coherent control experiments using analogous schemes. Such quantum control techniques may find broad application in suppressing leakage errors in a variety of quantum information architectures.
We investigate methods related to achieving interaction between photonic qubits. The first general approach to achieve this is to transfer photonic qubits to solid state systems, where the qubit interactions can then take place. The other approach is to enhance the strength of the photon-photon interaction. -- We first robustly study methods related to the first approach: in particular we focus on how to convert the photonic quantised excitation into an atomic excitation. The Stark-shift-chirped rapid adiabatic passage (SCRAP) technique in a three level Λ-type system is a coherent population transfer (CPT) technique similar to Stimulated Raman Adiabatic Passage (STIRAP), which in itself is closely related to electro-magnetically induced transparency (EIT). SCRAP has been shown to perform CPT with a high delity for a range of different detunings making SCRAP far more robust when there is large inhomogeneous broadenings present in the ensemble. We make use of optimum control techniques in order to optimise the standard SCRAP pulses so as to minimise the decrease in delity brought on by inhomogeneous broadenings of the transitions. Our result is that we can improve the average delity of population transfer over a wide range of detunings for both the ground to excited state detuning and the ground to target state detuning (two-photon detuning). -- Finally we consider the enhancement of photon-photon interactions and the implementation of an optical quantum controlled not (CNOT) gate via a cavity-QED setup. We explore the Nitrogen-vacancy centre in diamond as a suitable four-level tripod system in which to generate the cross-Kerr nonlinearity required to facilitate the strong interaction between the two fields (control and target) held in a cavity. We show that with an ultra-high quality factor cavity, and only a single NV centre strongly coupled to the trapped light, a suffciently large interaction can be generated between the two fields to obtain a conditional phase shift (CPS) in excess of the required π for the successful implementation of a CNOT gate. We also show that it is possible to use this system to create an entangled state of two macroscopically distinguishable states, that is a Schrödinger cat state, by using two weak coherent fields as input and making a measurement on the second field.
In this thesis, I report on experiments with cold 85Rb atoms in a far-detuned one-dimensional optical lattice. These experiments are focused on creating efficient coupling between the quantized vibrational states of atoms in the optical lattice, on controlling and maintaining coherence between the vibrational states, and on developing a spectroscopy method to characterize the decay of coherence. First, I present an experimental study of the application of simple and compound pulses consisting of time-dependent spatial translations to coupling vibrational states of ultracold 85Rb atoms in the optical\nlattice. Experimental results show that a square pulse consisting of lattice displacements and a delay is more efficient than single-step and Gaussian pulses. The square pulse can be seen as an example of coherent control. Numerical calculations are in strong agreement with the experimental results. In addition, it is shown numerically that the vibrational state coupling due to such lattice manipulations is more efficient in shallow lattices than in deep lattices, in which the coupling probability approaches the harmonic\noscillator limit. Next, the effectiveness of these pulses in reviving oscillations of atoms in vibrational superposition states using a pulse-echo technique is examined. Experimental results show that the square and Gaussian pulses result in higher echo amplitudes than the single-step pulse. These echo amplitudes are an order of magnitude larger than the echo amplitudes observed previously for the motional states of atoms in optical lattices.\nWith the aim of the optimized square echo pulse, echo amplitude is measured at much\nlonger times, where a surprising coherence freeze (plateau) is observed. To investigate \nmechanisms responsible for the observed echo decay and the coherence freeze, we developed\na new two-dimensional pump-probe spectroscopy technique to monitor the evolution of frequency-frequency correlations in the system, a necessary input for understanding the decay of coherence. Through this 2D technique, we have characterized the temporal decay of frequency memory and through our simulations we find that coherence freeze is related to the shape of this memory loss function. This technique is general in that it can be applied in a variety of quantum information candidate systems to probe the nature of their decoherence.
Abstract Effcient population transfer and motional state control are important for optical lattice clocks and precision experiments with lattice-trapped neutral atoms. Here we experimentally investigate adiabatic rapid passage (ARP) on the clock transition of a one-dimensional 87 Sr optical lattice clock and develop a mode-resolved model for ARP on motional sidebands. On the carrier transition, ARP enables robust internal-state transfer with a maximum excitation fraction of 0.98(2). On the blue motional sideband, ARP increases the maximum excitation fraction from 0.47(2) to 0.55(3), and the measured dynamics are consistently reproduced by the mode-resolved model. The model further predicts that the sideband transfer effciency can exceed 0.88 when the carrier Rabi frequency is increased to 15 kHz. Applying ARP to the red-sideband cooling reduces the axial mean vibrational occupation to approximately 0.038, corresponding to a motional ground-state population of 0.96. These results provide a quantitative basis for designing ARP excitation on motional sidebands and for optimizing sideband cooling in lattice-trapped atoms, with direct relevance to coherent state preparation in optical lattice clocks and related precision-measurement experiments in neutral atoms.
We investigate the effect of chirped excitation and the excitation detuning on the coherent control of population transfer and vibrational states in a four-level system. Density matrix equations are studied for optimally enhanced processes by considering specific parameters typical of oxazine systems. Our simulations show a strong dependence on the interplay between chirp and excitation detuning and predict enhancement factors up to 3.2 for population transfer and up to 38.5 for vibrational coherences of electronic excited states. The study of the dynamics of the populations and vibrational coherences involved in the four-level system allows an interpretation of the different enhancement/suppression processes observed.