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Homodyne quadrature laser interferometry for the characterization of low-frequency residual vibrational noise in cryogenic trapped-ion systems

Qingqing Qin, Bao-Quan Ou, Wei Wu, Yi Xie, Ting Chen, Chun-Wang Wu, Ping‐Xing Chen

Published Sep 18, 2024• 7 citations
Publisher

Abstract

Cryogenic trapped-ion systems (CTISs) have emerged as indispensable platforms for the advancement of quantum computation and precision measurement techniques. However, the sensitivity of these systems to vibrational noise, especially during the compression and expansion cycles of the cold head in a Gifford-McMahon cycle refrigerator (GMCR), poses a significant challenge. To mitigate this, we have crafted an innovative methodology for characterizing low-frequency residual vibrational noise in closed-cycle cryogenic trapped-ion systems. Our methodology is underpinned by a compact homodyne quadrature laser interferometer (HQLI) vibrometer system that boasts nanometer-scale accuracy. This state-of-the-art system leverages elliptic curve fitting to rectify nonlinear noise artifacts and applies an inverse tangent function to demodulation phase techniques, enabling accurate vibrational displacement measurements. Unlike the conventional approach, our scheme circumvents the introduction of extraneous vibrational noise associated with piezoelectric ceramic mirrors, which are conventionally employed to track target vibrations for locking the interference signal intensity in the reference arm. This innovation not only improves the overall CTIS performance but is also significantly applied to characterize the practical realization of quantum computation and precision measurement.

DOI
10.1364/oe.538558

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Cryogenic trapped-ion systems (CTISs) have emerged as indispensable platforms for the advancement of quantum computation and precision measurement techniques. However, the sensitivity of these systems to vibrational noise, especially during the compression and expansion cycles of the cold head in a Gifford-McMahon cycle refrigerator (GMCR), poses a significant challenge. To mitigate this, we have crafted an innovative methodology for characterizing low-frequency residual vibrational noise in closed-cycle cryogenic trapped-ion systems. Our methodology is underpinned by a compact homodyne quadrature laser interferometer (HQLI) vibrometer system that boasts nanometer-scale accuracy. This state-of-the-art system leverages elliptic curve fitting to rectify nonlinear noise artifacts and applies an inverse tangent function to demodulation phase techniques, enabling accurate vibrational displacement measurements. Unlike the conventional approach, our scheme circumvents the introduction of extraneous vibrational noise associated with piezoelectric ceramic mirrors, which are conventionally employed to track target vibrations for locking the interference signal intensity in the reference arm. This innovation not only improves the overall CTIS performance but is also significantly applied to characterize the practical realization of quantum computation and precision measurement.
Abstract Cryogenic ion traps offer substantial advantages over their room-temperature counterparts, particularly in terms of stable ion confinement and cooling. However, this technological advancement has introduced a significant challenge, namely the generation of additional vibrational noise. This noise is pronounced during the compression and expansion phases of the Gifford–McMahon cycle refrigerator and stems from the mechanical operation of the cold head. The residual vibrational noise can modulate the Rabi oscillation frequency, thereby compromising the fidelity of the quantum logic gate. In this study, we quantitatively assess the impact of residual vibrational noise and introduce an innovative strategy for its mitigation. This strategy was designed to reduce superimposed potential fluctuations within a cryogenic surface electrode ion trap. The measured residual vibrational noise was used for real-time feedback control. Addressing the inverse determination of the compensating potential for a stable superimposed trapping potential is an inherently ill-posed problem considering known measurement noise results. By applying quadratic programming, we numerically calculated the optimal time series for the compensation potential. An ensemble of these compensation voltages was applied in real time to the static compensation electrodes. Although this method is in the theoretical stage, we believe that it can effectively suppress the translation induced by vibrational noise and foster the creation of a stable superimposed harmonic potential. The deployment of this technique is expected to substantially improve the accuracy of quantum operations, thereby fueling the evolution of quantum technologies.
We describe the design, commissioning, and operation of an ultra-low-vibration closed-cycle cryogenic ion trap apparatus. One hundred lines for low-frequency signals and eight microwave/radio frequency coaxial feed-lines offer the possibility of implementing a small-scale ion-trap quantum processor or simulator. With all supply cables attached, more than 1.3 W of cooling power at 5 K is still available for absorbing energy from electrical pulses introduced to control ions. The trap itself is isolated from vibrations induced by the cold head using a helium exchange gas interface. The performance of the vibration isolation system has been characterized using a Michelson interferometer, finding residual vibration amplitudes on the order of 10 nm rms. Trapping of 9Be+ ions has been demonstrated using a combination of laser ablation and photoionization.
Trapped ions are one of the leading platforms for building scalable quantum information processors. Current ion traps run on less than 100 qubits. A useful quantum computer needs to operate thousands or even millions of qubits. If systems reach gate fidelities that allow for quantum error correction, gate errors below the physical fidelity can be reached, which is important for scaling. The most promising platform for scaling up ion-based quantum computers are surface electrode traps in connection with the so-called QCCD (Quantum Charge Coupled Device) architecture. In an evolution of the standard (laser-based) approach to quantum logic gates, gates can be performed by applying an oscillating magnetic near-field gradient to the ions. Current fidelities are about one order of magnitude away from reaching the fault tolerant threshold with no fundamental limitations in sight. Scaling QCCDs is impeded by heating rates of the ions as well as vacuum quality. Ions have to be stored for at least as long as it takes for an algorithm to run and subsequent readout. Collisions with background gas and heating can expel ions from the trap. The microwave near-field approach of driving gates benefits from ions that are trapped close to the trap surface. Unfortunately, heating becomes more prominent near the surface. A cryogenic environment reduces the background pressure by several orders of magnitude and the kinetic energy of gas molecules by two orders of magnitude. Heating rates in a cryogenic trap are about two orders of magnitude lower than in a room temperature trap with otherwise equal physical properties. To operate a QCCD processor, it is required to employ phase-stable Raman laser beams. The cryogenic design of the apparatus needs to take into account the resulting requirements for ultra-low vibration amplitudes. This is particularly relevant for closed-cycle cooling systems, which are desirable from an economic point of view compared to liquid cryostats that boil off helium, but which also feature moving mechanical parts that can introduce a serious amount of vibrations. Here, we present a vibration isolated closed cycle Gifford-McMahon cryocooler with record low vibration amplitudes of 29 nm (RMS=7.8 nm) in the vertical and 51 nm (RMS=13.5 nm) in the horizontal direction. It contains a self-sustained inner vacuum chamber that houses the trap. It features 100 DC connections, 10 of which are able to carry up to 1 A of current and 8 high frequency lines. At 5 K, we can apply continuous 3.4 W of microwave power continuously at 1 GHz to the trap electrodes without heating the system. This is about 5.8 times more than state of the art near-field gates require. We also present the laser systems required to for single-shot ablation loading and Doppler cooling of Be ions: a 70 mW 313 nm Dopper cooling laser, a 1064 nm ns-pulse laser for ablation of neutral beryllium atoms and a 235 nm laser for ionizing them. The detection system features an in vacuum imaging system on a cryogenic 3D translation stage that is able to scan and image the complete surface of an ion trap. The light can be detected on a photomultiplier tube or spatially resolved on an EMCCD camera. Our trap features a meander structure for driving gates and can trap up to 5 ions of which we, so far, did not lose any due to background gas collisions. This hints at a vacuum pressure of 1e-12 mbar or lower. The demonstrated system could hold a cryogenic QCCD chip with a few 10 qubits
Cryogenic environments benefit ion trapping experiments by offering lower motional heating rates, collision energies, and an ultrahigh vacuum (UHV) environment for maintaining long ion chains for extended periods of time. Mechanical vibrations caused by compressors in closed-cycle cryostats can introduce relative motion between the ion and the wavefronts of lasers used to manipulate the ions. Here, we present a novel ion trapping system where a commercial low-vibration closed-cycle cryostat is used in a custom monolithic enclosure. We measure mechanical vibrations of the sample stage using an optical interferometer, and observe a root-mean-square relative displacement of 2.4 nm and a peak-to-peak displacement of 17 nm between free-space beams and the trapping location. We packaged a surface ion trap in a cryopackage assembly that enables easy handling while creating a UHV environment for the ions. The trap cryopackage contains activated carbon getter material for enhanced sorption pumping near the trapping location, and source material for ablation loading. Using171^{171}171Yb+^{+}+as our ion, we estimate the operating pressure of the trap as a function of package temperature using phase transitions of zig-zag ion chains as a probe. We measured the radial mode heating rate of a single ion to be 13 quanta/s on average. The Ramsey coherence measurements yield 330-ms coherence time for counter-propagating Raman carrier transitions using a 355-nm mode-locked pulse laser, demonstrating the high optical stability.
Balanced homodyne interferometry is a well-known detection technique that allows for sensitive characterization of light fields. Conventionally a homodyne interferometer is operated by locking the relative phase of a reference beam to the signal beam by means of an active feedback loop. A less often used method is to perform a slow continuous modulation of the reference beam arm length that corresponds to averaging all relative phases during the measurement.Here we show theoretically and experimentally that this quadrature averaging can be advantageous in estimating the parameters of a resonant optical cavity. We demonstrate that the averaging turns the transduction function, from cavity frequency fluctuations into the interferometer signal, into a simple function of the laser detuning that, notably, does not depend on the parameters of possible non-resonant channels present in the system. The method needs no active feedback and gives results that are easy to interpret. Moreover, the phase-averaged measurement allows to characterize the absolute magnitude of a cavity frequency modulation.
Balanced homodyne interferometry is a well-known detection technique that allows for sensitive characterization of light fields. Conventionally a homodyne interferometer is operated by locking the relative phase of a reference beam to the signal beam by means of an active feedback loop. A less often used method is to perform a slow continuous modulation of the reference beam arm length that corresponds to averaging all relative phases during the measurement. Here we show theoretically and experimentally that this quadrature averaging can be advantageous in estimating the parameters of a resonant optical cavity. We demonstrate that the averaging turns the transduction function, from cavity frequency fluctuations into the interferometer signal, into a simple function of the laser detuning that, notably, does not depend on the parameters of possible nonresonant channels present in the system. The method needs no active feedback and gives results that are easy to interpret. Moreover, the phase-averaged measurement allows characterization of the absolute magnitude of a cavity frequency modulation.