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Abstract Interferometry with thermal cold atom clouds provides high particle flux and low quantum projection noise but is limited by the rapid reduction of fringe contrast. We propose an improved method based on temporally shaped pulses to address the issue of the off-resonance dispersion and enhance the contrast. Theoretical analysis and construct...
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... illustrate the principle of constructing and evaluat- ing a shaped pulse, a schematic of the response spectrum is illustrated in Figure 2, where the horizontal and ver- tical axes are the detuning and corresponding coefficient in atomic state |e, respectively. The black line denotes the amplitude spectrum |c e | while the red curve denotes the phase spectrum ϕ. ...
Citations
... The measurement performance is highly dependent on the fidelity of the Raman transition process: imperfect pulses cause errors that affect the accuracy and precision of a cold-atom inertial sensor [13,14]. Imperfection in the mirror process largely affects the contrast of the interferometric signal [15], while in the beam-splitting and recombining processes they mainly result in the introduction of phase errors [13,16,17]. ...
We present a methodology for the design of optimal Raman beam-splitter pulses suitable for cold atom inertial sensors. The methodology, based on time-dependent perturbation theory, links optimal control and the sensitivity function formalism in the Bloch sphere picture, thus providing a geometric interpretation of the optimization problem. Optimized pulse waveforms are found to be more resilient than conventional beam-splitter pulses and ensure a near-flat superposition phase for a range of detunings approaching the Rabi frequency. As a practical application, we simulated the performance of an optimized Mach-Zehnder interferometer in terms of scale-factor error and bias induced by interpulse laser intensity variations. Our findings reveal enhancements compared to conventional interferometers operating with constant-power beam-splitter pulses.
... Figure 1(a) shows a block diagram of a multi-channel RF generator for use with a CAI, and Fig. 1(b) shows the pulse sequences needed by an atom-interferometer gyroscope, in which the minimum pulse width is only a few microseconds. To improve the performance of an atom interferometer, the traditional rectangular pulses can be replaced by shaped pulses; 17,18 however, in such a system, the switching time of the RF signal must be less than 1 μs. As a consequence, a multi-channel RF pulse-sequence generator with fast-switching capability is indispensable for creating high-performance CAIs. ...
Cold-atom interferometers have matured into a powerful tool for fundamental physics research, and they are currently moving from realizations in the laboratory to applications in the field. A radio frequency (RF) generator is an indispensable component of these devices for controlling lasers and manipulating atoms. In this work, we developed a compact RF generator for fast switching and sweeping the frequencies and amplitudes of atomic-interference pulse sequences. In this generator, multi-channel RF signals are generated using a field-programmable gate array (FPGA) to control eight direct digital synthesizers (DDSs). We further propose and demonstrate a method for pre-loading the parameters of all the RF pulse sequences to the DDS registers before their execution, which eliminates the need for data transfer between the FPGA and DDSs to change RF signals. This sharply decreases the frequency-switching time when the pulse sequences are running. Performance characterization showed that the generated RF signals achieve a 100 ns frequency-switching time and a 40 dB harmonic-rejection ratio. The generated RF pulse sequences were applied to a cold-atom-interferometer gyroscope, and the contrast of atomic interference fringes was found to reach 38%. This compact multi-channel generator with fast frequency/amplitude switching and/or sweeping capability will be beneficial for applications in field-portable atom interferometers.
... The measurement performance is highly dependent on the fidelity of the Raman transition process: imperfect pulses cause errors that affect the accuracy and precision of a cold atom inertial sensor [12,13]. Imperfection in the mirror process largely affects the contrast of the interferometric signal [14], while in the beam-splitting and recombining processes they mainly result in the introduction of phase errors [12,15,16]. ...
We present a methodology for the design of optimal Raman beam-splitter pulses suitable for cold atom inertial sensors. The methodology, based on time-dependent perturbation theory, links optimal control and the sensitivity function formalism in the Bloch sphere picture, thus providing a geometric interpretation of the optimization problem. Optimized pulse waveforms are found to be more resilient than conventional beam-splitter pulses and ensure a near-flat superposition phase for a range of detunings approaching the Rabi frequency. As a practical application, we have simulated the performance of an optimized Mach-Zehnder interferometer in terms of scale-factor error and bias induced by inter-pulse laser intensity variations. Our findings reveal enhancements compared to conventional interferometers operating with constant-power beam-splitter pulses.
... One promising solution is to engineer more advanced Bragg pulses that are robust to such variations using quantum optimal control techniques. In atom interferometry, quantum control schemes including composite pulses [49][50][51], shaped pulses [52,53], adiabatic rapid passage (ARP) [54], and numerical optimal control [55][56][57] have been applied to Raman transitions with alkalis, while Floquet pulse engineering has been applied to single-photon atom optics on the 1 S 0 → 3 P 1 transition of Sr [58]. Existing optimal control applications to Bragg diffraction have explored numerical optimization of single order pulses in combination with higher order ARP [59][60][61]. ...
Multi-photon Bragg diffraction is a powerful method for fast, coherent momentum transfer of atom waves. However, laser noise, Doppler detunings, and cloud expansion limit its efficiency in large momentum transfer (LMT) pulse sequences. We present simulation studies of robust Bragg pulses developed through numerical quantum optimal control. Optimized pulse performance under noise and cloud inhomogeneities is analyzed and compared to analogous Gaussian and adiabatic rapid passage pulses in simulated LMT Mach-Zehnder interferometry sequences. The optimized pulses maintain robust population transfer and phase response over a broader range of noise, resulting in superior contrast in LMT sequences with thermal atom clouds and intensity inhomogeneities. Large optimized LMT sequences use lower pulse area than Gaussian pulses, making them less susceptible to spontaneous emission loss. The optimized sequences maintain over five times better contrast with tens of $\hbar k$ momentum separation and offers more improvement with greater LMT. Such pulses could allow operation of Bragg atom interferometers with unprecedented sensitivity, improved contrast, and hotter atom sources.
... One promising solution is to engineer more advanced Bragg pulses that are robust to such variations using quantum optimal control techniques. In atom interferometry, quantum control schemes including composite pulses [43][44][45], shaped pulses [46,47], adiabatic rapid passage (ARP) [48], and numerical optimal control [49][50][51] have been applied to Raman transitions with alkalis, while Floquet pulse engineering has been applied to single-photon atom optics on the 1 S 0 → 3 P 1 transition of Sr [52]. Existing optimal control applications to Bragg diffraction have explored numerical optimization of single order pulses in combination with higher order ARP [53][54][55]. ...
Multi-photon Bragg diffraction is a powerful method for fast, coherent momentum transfer of atom waves. However, laser noise, Doppler detunings, and cloud expansion limit its efficiency in large momentum transfer (LMT) pulse sequences. We present simulation studies of robust Bragg pulses developed through numerical quantum optimal control. Optimized pulse performance under noise and cloud inhomogeneities is analyzed and compared to analogous Gaussian and adiabatic rapid passage (ARP) pulses in simulated LMT Mach-Zehnder interferometry sequences. The optimized pulses maintain robust population transfer and phase response over a broader range of noise, resulting in superior contrast in LMT sequences with thermal atom clouds and intensity inhomogeneities. Large optimized LMT sequences use lower pulse area than Gaussian pulses, making them less susceptible to spontaneous emission loss. The optimized sequences maintain over five times better contrast with tens of $\hbar k$ momentum separation and offers more improvement with greater LMT. Such pulses could allow operation of Bragg atom interferometers with unprecedented sensitivity, improved contrast, and hotter atom sources.
... Comb tailoring With standard pulse shaping techniques [33][34][35], interesting pulse properties can be designed by tailoring the spectrum envelope. For example, introducing a power ratio α < 1 produces smoother plateaus [ Fig. 2, right], which ensures that the singleatom π -time, τ poly π = π/δω [see Sect. ...
Coherent manipulation of atoms with atom-optic light pulses is central to atom interferometry. Achieving high pulse efficiency is essential for enhancing fringe contrast and sensitivity, in particular for large-momentum transfer interferometers which use an increased number of pulses. We perform an investigation of optimizing the frequency domain of pulses by using tailored polychromatic light fields, and demonstrate the possibility to deliver high-efficiency and resilient atom-optic pulses even in the situation of inhomogeneous atomic clouds and laser beams. We find that this approach is able to operate over long interrogation times despite spontaneous emission and to achieve experimentally relevant pulse efficiencies for clouds up to 100μK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$100~\mu \text{K}$\end{document}. This overcomes some of the most stringent barriers for large-momentum transfer and has the potential to reduce the complexity of atom interferometers. We show that polychromatic light pulses could enhance single-photon-based large-momentum transfer atom interferometry—achieving 850ħk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$850\,\hbar k$\end{document} of momentum splitting with experimentally accessible parameters, which represents a significant improvement over the state-of-the art. The benefits of the method extend beyond atom interferometry and could enable groundbreaking advances in quantum state manipulation.
... In the field of atom interferometry, quantum control schemes including composite pulses [67,68], shaped pulses [57,69], adiabatic rapid passage [44,70], and numerical optimal control [71][72][73][74] have been applied to Raman and Bragg transitions with alkalis. In this paper, we report simulation studies of numerical optimal control's applications to clock interferometry with 87 Sr. ...
Strontium clock atom interferometry is a promising new technique, with multiple experiments under development to explore its potential for dark matter and gravitational wave detection. In these detectors, large momentum transfer (LMT) using sequences of many laser pulses is necessary, and thus high fidelity of each pulse is important since small infidelities become magnified. Quantum Optimal Control (QOC) is a framework for developing control pulse waveforms that achieve high fidelity and are robust against experimental imperfections. Resonant single-photon transitions using the narrow clock transition of strontium involve significantly different quantum dynamics than more established atom interferometry methods based on far-detuned two-photon Raman or Bragg transitions, which leads to new opportunities and challenges when applying QOC. Here, we study QOC pulses for strontium clock interferometry and demonstrate their advantage over basic square pulses (primitive pulses) and composite pulses in terms of robustness against multiple noise channels. This could improve the scale of large momentum transfer in Sr clock interferometers, paving the way to achieve these scientific goals.
... The contrast improves with a selection pulse that has a Rabi frequency (Ω s.p. ) smaller than the one used for the interferometric sequence (Ω i.s. ) (Fig. 6). An alternative way to improve the contrast is to make use of modulated pulses [32]. In the opposite extreme case (σ v T ≫ w a , corresponding to T ≫ 80 ms at a temperature of 3 µK), the atoms expand radially with w a (t) ≃ σ v T and the normalized beam diameter s decreases with time. ...
The laser beam waist has an impact both in the sensitivity and systematic effects present in gravimetry and atom interferometry in general. In this paper we consider how different effects contribute to both aspects in order to make a better selection of the radius of the Raman beam given a particular laser power available. A large beam waist reduces systematic effects coming from wavefront curvature and Gouy phase contributions and improves the fringe contrast due to reduced intensity gradients. On the other hand, a large waist gives a smaller Rabi frequency, which lowers the sensitivity by reducing the fraction of atoms in the selected velocity range. Considering all contributions, we find that systematic effects usually have a dominant role in selecting a beam waist.
... The detected fraction of atoms in the excited state following an interferometer sequence is given by the integral of Equation 3.11 over the distribution of atoms in the sample. This integral may be computed analytically [108,109], or else using a Monte Carlo approach [44]. ...
... This is equivalent to requiring the combined phase shift due to the pulse sequence, ∆φ, to be fixed or cancelled by the pulses for every atom. If ∆φ varies from atom to atom, the resulting contrast after thermal averaging will be washed out due to the contribution of fringes with different phases [108] and a phase error may be introduced into the interferometric measurement. phases φ(δ 1 ) and φ(δ 2 ). ...
... The phase shift following the conventional π/2 − π − π/2 sequence is Doppler-insensitive providing the Rabi rate does not vary from pulse to pulse [109]. If the interferometer phase varies with the Raman detuning, this implies that in an ensemble of atoms with a velocity spread, different atoms will exit the interferometer with different phases [108]. This can lead to a reduction in fringe visibility when the output signal is averaged over the entire atom cloud. ...
Atom interferometric sensors can enable extremely precise measurements of inertial motion and external fields by manipulating and interfering atomic states using pulses of laser light. However, like many experiments that require the coherent control of a quantum system, the interaction fidelity is limited by inhomogeneities in the control fields. Variations in atomic velocity and laser intensity lead different atoms to experience different interactions under the same pulse, reducing the interference fringe contrast, introducing bias, and limiting the sensitivity. We present the theoretical design and experimental demonstration of pulses for atom interferometry which compensate inhomogeneities in atomic velocity and laser intensity. By varying the laser phase throughout a pulse and choosing an appropriate fidelity measure to be maximised, pulses are optimised by adapting optimal control techniques originally designed for nuclear magnetic resonance applications. We show using simulations that optimised pulses significantly improve the fidelity of interferometer operations and verify this experimentally using Raman transitions within a cold sample of 85Rb atoms. We demonstrate a robust state-transfer pulse that achieves a fidelity of 99.8(3)% in a ∼ 35 µK sample and obtain a threefold increase in the fringe contrast using a full sequence of optimised pulses. Many of the pulse shapes found by optimal control are simple and symmetrical, and we show that certain symmetries are integral to error compensation. By systematically exploring the dependence of these solutions on the model and optimisation parameters, we demonstrate a stability which underlines the general applicability of optimised pulses to a range of interferometer configurations. Finally, we introduce and computationally analyse a novel theoretical approach to improve the sensitivity of large-momentum-transfer (LMT) interferometers, whereby “biselective” pulses are optimised to track the changing resonance conditions encountered in extended pulse sequences that are designed to increase the measurement sensitivity. When conventional pulses of steady phase are used, the interference contrast decays rapidly as extra pulses are added because of the change in resonance. Using numerical simulations, we show that bi-selective pulses maintain interaction fidelity throughout extended pulse sequences, allowing significant increases in the sensitivity that may be obtained using LMT.
... is a phase factor introduced to the output by the atom-light interactions themselves. This should be minimised, or at least fixed, over a range a Raman detunings δ L and Rabi frequencies Ω R so that the signal has the same phase for all atoms and the fringes are not washed out when averaged over a thermal ensemble as they are with some pulses [2,172]. ...
... have not yet experimented with varying is the pulse amplitude. It is well known, and can be shown by Fourier analysis, that pulses with smoothly varying amplitude profiles are more robust to highfrequency phase noise of the interferometry beams [172,209] and can be used to realise sharper resonances [210]. As we are able to smoothly vary the pulse amplitude in our experiment, it is a logical step to include this as a control parameter in the GRAPE algorithm. ...
Ultracold samples of laser-cooled atoms are quantum systems over which modern atomic physicists can exert exquisite control. Largely decoupled from their environment, they can act as near-ideal test masses for inertial sensors based on atom interferometry and are well suited to experiments in coherent control of quantum systems that probe the fundamental nature of quantum mechanics and pave the way for practical quantum simulation and computation.
This thesis details a series of experimental results that arise from the coherent control of rubidium atoms with laser light, focusing on the interplay between these interactions and atomic velocities; the laser frequency an atom ‘sees’ is Doppler shifted according to its velocity, while conservation of momentum dictates that, in exchanging photons with a laser, an atom’s velocity is altered.
Coherent light–atom interactions can thus be tailored either to measure or to narrow the spread of velocities in an ultracold atomic gas. Alternatively, it can be desirable to design interactions that are homogeneous across a large spread of atomic velocities. All of these aspects are explored in this thesis.
The velocity-sensitive interactions that lie at the heart of atom-interferometric inertial sensors are reexamined in a manner that yields considerable insight into the underlying processes and culminates in a novel, precise and elegant technique for measuring the velocity of ultracold atoms that is used to reveal the Gaussian nature of the velocity spread in a cloud with an effective temperature of 18.7(6) µK, undistorted by artefacts that plague other methods.
Furthermore, optimal control techniques are applied to the problem of coherently and uniformly manipulating the quantum states of atoms in an ensemble with a large spread of velocities, even subject to variations in laser intensity. A broadband inversion pulse is demonstrated to change the internal state of 99.8(3) % of atoms in a ∼35 µK ensemble and — for the first time — this technique is used to optimise an entire atom interferometry sequence, yielding a threefold enhancement in the measurement contrast.
Finally, a version of grey molasses cooling — in which atoms accumulate in velocity-dependent ‘dark’ states, narrowing their momentum spread and increasing their phase space density — is demonstrated with phase-coherent cooling beams; dark states that exist in this system prove to be particularly resilient to the spatially varying light shifts that are present in an optical dipole trap, and this is used both to enhance the number of atoms loaded into such a trap — by a factor of 7 compared to loading from a conventional optical molasses — and to further cool them once they are loaded in a technique that has promising prospects for the rapid production of ultracold, trapped, atoms.<br/
