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Scientific Reports

Quantum Zeno Effect assisted Spectroscopy of a single trapped Ion

Akira Ozawa, Josue Davila-Rodriguez, Theodor W. Hänsch, Thomas Udem

Published Jul 9, 2018• 5 citations
Publisher

Abstract

The quantum Zeno effect (QZE) is not only interesting as a manifestation of the counterintuitive behavior of quantum mechanics, but may also have practical applications. When a spectroscopy laser is applied to target atoms or ions prepared in an initial state, the Rabi flopping of an auxiliary transition sharing one common level can be inhibited. This effect is found to be strongly dependent on the detuning of the spectroscopy laser and offers a sensitive spectroscopy signal which allows for high precision spectroscopy of transitions with a small excitation rate. We demonstrate this method with direct frequency comb spectroscopy using the minute power of a single mode to drive a dipole allowed transition in a single trapped ion. Resolving the individual modes of the frequency comb demonstrates that the simple instantaneous quantum collapse description of the QZE can not be applied here, as these modes need several pulses to build up.

DOI
10.1038/s41598-018-28824-w

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Direct comb spectroscopy by quantum-Zeno-effect assisted detection

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Summary form only given. The time evolution of a quantum system can be entirely prohibited by applying frequent quantum measurements which repeatedly introduce wavefunction collapse. The effect is typically termed Quantum Zeno Effect (QZE) which was originally proposed to inhibit the decay of an unstable particle through repeated measurements [1], and experimentally demonstrated later with trapped ions [2]. The QZE is not only interesting as a clear manifestation of the counterintuitive behaviour of quantum mechanics, but may also have practical applications: we show QZE-assisted detection is useful for high precision spectroscopy. Fig.1(a) shows the level scheme of an atomic (ionic) system under consideration. The levels | ↑ 〉 and | ↓ 〉 possess long lifetimes and form a qubit which can be coherently controlled via microwave pulses. After initial state preparation into ground state | ↑ 〉, the system is exposed to a π microwave-pulse on the | ↑ 〉 →|↓〉 transition. In the scheme of QZE-assisted spectroscopy, at the same time as the system is exposed to the microwave-pulses, a spectroscopy laser which probes optical transitions of | ↓ 〉 ↔ |e1〉 and/or | ↑ 〉 ↔ |e2〉 is also present. If the spectroscopy laser introduce spontaneous decay from |e1〉 or |e2〉 states, the system experiences “quantum measurement” and the wave function spanned by | ↑〉 and | ↓ 〉 states collapses into one of the two bases of | ↑ 〉 or | ↓ 〉. In its strongest form when the “quantum measurement” is performed frequent enough, it completely prevents the transfer of population from | ↑ 〉 to | ↓ 〉. The effect is found to be strongly dependent on the detuning of the spectroscopy laser and offers a sensitive spectroscopy signal which allows for high precision spectroscopy of transitions with small excitation rate. An example is direct frequency comb spectroscopy of a single photon transition where only the minute power contained in a single comb mode contributes to the excitation. In this work, we demonstrate QZE-assisted spectroscopy of single25Mg+ions trapped in a Paul trap. The spectroscopy laser is a deep-ultraviolet (DUV) frequency comb at 280 nm and generated by frequency tripling a Ti:sapphire mode-locked ring laser. We choose to use a DUV frequency comb as a spectroscopy laser because it can readily demonstrate the main advantages of the technique, which are higher sensitivity and smaller background noise. Typical spectroscopy signal for the QZE-assisted spectroscopy is shown in Fig. 1(b). The remaining population of the initial state | ↑ 〉 after the spectroscopy period is plotted for different detunings of the spectroscopy laser, which is a measure for the strength of the QZE introduced by the spectroscopy laser. The repeating structure with a period that corresponds to comb mode spacing reflects the mode structure of the frequency comb. Pairs of lines are observed which correspond to | ↑ 〉 ↔ |e2〉 and | ↓ 〉 ↔ |e1〉 transitions. The latter transition corresponds to the “null measurement” case where the observation of no photon scattering events from the spectroscopy laser confirms the existence of no population in the state and thus serves as a quantum measurement. Under our experimental conditions, we found that even 50 μw of average power of frequency comb, which corresponds to approximately 1.5 nw per comb mode, was sufficient to introduce significant QZE and detect the spectroscopy signal with high signal to noise ratio. The QZE-assisted detection is expected to be useful for high precision spectroscopy experiments in extreme-ultraviolet regions where even smaller comb power is available.

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Xiufeng Cao, Qing Ai, C. P. Sun +1 more

We propose a strategy to demonstrate the transition from the quantum Zeno effect (QZE) to the anti-Zeno effect (AZE) by modulating the central frequency of the cavity mode. Our results are obtained without using the rotating wave approximation (RWA), and the initial state (a dressed state) is easy to prepare. When the central frequency of the cavity mode is resonant with the qubit energy level spacing, the normalized decay rate of the qubit is lower than 1, which manifests the QZE. However, when the cavity frequency is detuned from resonance, the normalized decay rate becomes larger than 1, which corresponds to the AZE. The change from the QZE to the AZE, by just varying the central frequency of the cavity mode, should allow to distinguish these two different effects. Moreover, we find that in the presence of both qubit's intrinsic bath and the cavity bath, the emergence of the QZE and the AZE behaviors relies not only on the match between the qubit energy level spacing and the central frequency of the cavity mode, but also on the coupling strength between the qubit and the cavity mode.

arXiv:1011.3862•Nov 17, 2010•0 citations
The quantum Zeno effect (QZE) is not only interesting as a manifestation of the counterintuitive behavior of quantum mechanics, but may also have practical applications. When a spectroscopy laser is applied to target atoms or ions prepared in an initial state, the Rabi flopping of an auxiliary transition sharing one common level can be inhibited. This effect is found to be strongly dependent on the detuning of the spectroscopy laser and offers a sensitive spectroscopy signal which allows for high precision spectroscopy of transitions with a small excitation rate. We demonstrate this method with direct frequency comb spectroscopy using the minute power of a single mode to drive a dipole allowed transition in a single trapped ion. Resolving the individual modes of the frequency comb demonstrates that the simple instantaneous quantum collapse description of the QZE can not be applied here, as these modes need several pulses to build up.
Summary form only given. The time evolution of a quantum system can be entirely prohibited by applying frequent quantum measurements which repeatedly introduce wavefunction collapse. The effect is typically termed Quantum Zeno Effect (QZE) which was originally proposed to inhibit the decay of an unstable particle through repeated measurements [1], and experimentally demonstrated later with trapped ions [2]. The QZE is not only interesting as a clear manifestation of the counterintuitive behaviour of quantum mechanics, but may also have practical applications: we show QZE-assisted detection is useful for high precision spectroscopy. Fig.1(a) shows the level scheme of an atomic (ionic) system under consideration. The levels | ↑ 〉 and | ↓ 〉 possess long lifetimes and form a qubit which can be coherently controlled via microwave pulses. After initial state preparation into ground state | ↑ 〉, the system is exposed to a π microwave-pulse on the | ↑ 〉 →|↓〉 transition. In the scheme of QZE-assisted spectroscopy, at the same time as the system is exposed to the microwave-pulses, a spectroscopy laser which probes optical transitions of | ↓ 〉 ↔ |e1〉 and/or | ↑ 〉 ↔ |e2〉 is also present. If the spectroscopy laser introduce spontaneous decay from |e1〉 or |e2〉 states, the system experiences “quantum measurement” and the wave function spanned by | ↑〉 and | ↓ 〉 states collapses into one of the two bases of | ↑ 〉 or | ↓ 〉. In its strongest form when the “quantum measurement” is performed frequent enough, it completely prevents the transfer of population from | ↑ 〉 to | ↓ 〉. The effect is found to be strongly dependent on the detuning of the spectroscopy laser and offers a sensitive spectroscopy signal which allows for high precision spectroscopy of transitions with small excitation rate. An example is direct frequency comb spectroscopy of a single photon transition where only the minute power contained in a single comb mode contributes to the excitation. In this work, we demonstrate QZE-assisted spectroscopy of single25Mg+ions trapped in a Paul trap. The spectroscopy laser is a deep-ultraviolet (DUV) frequency comb at 280 nm and generated by frequency tripling a Ti:sapphire mode-locked ring laser. We choose to use a DUV frequency comb as a spectroscopy laser because it can readily demonstrate the main advantages of the technique, which are higher sensitivity and smaller background noise. Typical spectroscopy signal for the QZE-assisted spectroscopy is shown in Fig. 1(b). The remaining population of the initial state | ↑ 〉 after the spectroscopy period is plotted for different detunings of the spectroscopy laser, which is a measure for the strength of the QZE introduced by the spectroscopy laser. The repeating structure with a period that corresponds to comb mode spacing reflects the mode structure of the frequency comb. Pairs of lines are observed which correspond to | ↑ 〉 ↔ |e2〉 and | ↓ 〉 ↔ |e1〉 transitions. The latter transition corresponds to the “null measurement” case where the observation of no photon scattering events from the spectroscopy laser confirms the existence of no population in the state and thus serves as a quantum measurement. Under our experimental conditions, we found that even 50 μw of average power of frequency comb, which corresponds to approximately 1.5 nw per comb mode, was sufficient to introduce significant QZE and detect the spectroscopy signal with high signal to noise ratio. The QZE-assisted detection is expected to be useful for high precision spectroscopy experiments in extreme-ultraviolet regions where even smaller comb power is available.
We experimentally demonstrate the quantum anti-Zeno effect in a two-level system based on a single trapped ion 40 Ca + . In the large detuning regime, we show that the transfer from the ground state to the excited state can be remarkably enhanced by the inserted projection measurements. The inserted measurements in our experiment are realized by the electron shelving technique. Compared to the ideal projection measurement, which makes the quantum state collapse instantaneously, a practical electron shelving process needs a finite time duration. The minimum time for this collapse process is shown to be inversely proportional to the square of the coupling strength between the measurement laser and the system.
The quantum Zeno effect (QZE) predicts a slow-down of the time development of a system under rapidly repeated ideal measurements, and experimentally this was tested for an ensemble of atoms using short laser pulses for non-selective state measurements. Here we consider such pulses for selective measurements on a single system. Each probe pulse will cause a burst of fluorescence or no fluorescence. If the probe pulses were strictly ideal measurements, the QZE would predict periods of fluorescence bursts alternating with periods of no fluorescence (light and dark periods) which would become longer and longer with increasing frequency of the measurements. The non-ideal character of the measurements is taken into account by incorporating the laser pulses in the interaction, and this is used to determine the corrections to the ideal case. In the limit, when the time between the laser pulses goes to zero, no freezing occurs but instead we show convergence to the familiar macroscopic light and dark periods of the continuously driven Dehmelt system. An experiment of this type should be feasible for a single atom or ion in a trap
The quantum Zeno effect (QZE) predicts a slow-down of the time development of a system under rapidly repeated ideal measurements, and experimentally this was tested for an ensemble of atoms using short laser pulses for non-selective state measurements. Here we consider such pulses for selective measurements on a single system. Each probe pulse will cause a burst of fluorescence or no fluorescence. If the probe pulses were strictly ideal measurements, the QZE would predict periods of fluorescence bursts alternating with periods of no fluorescence (light and dark periods) which would become longer and longer with increasing frequency of the measurements. The non-ideal character of the measurements is taken into account by incorporating the laser pulses in the interaction, and this is used to determine the corrections to the ideal case. In the limit, when the time, , between the laser pulses goes to zero, no freezing occurs but instead we show convergence to the familiar macroscopic light and dark periods of the continuously driven Dehmelt system. An experiment of this type should be feasible for a single atom or ion in a trap.
The quantum Zero effect is the inhibition of transitions between quantum states by frequent measurements of the state. The inhibition arises because the measurement causes a collapse (reduction) of the wave function. If the time between measurements is short enough, the wave function usually collapses back to the initial state. We have observed this effect in an rf transition between two 9^{9}9Be+{\mathrm{Be}}^{+}Be+ ground-state hyperfine levels. The ions were confined in a Penning trap and laser cooled. Short pulses of light, applied at the same time as the rf field, made the measurements. If an ion was in one state, it scattered a few photons; if it was in the other, it scattered no photons. In the latter case the wave-function collapse was due to a null measurement. Good agreement was found with calculations.
We propose a strategy to demonstrate the transition from the quantum Zeno effect (QZE) to the anti-Zeno effect (AZE) by modulating the central frequency of the cavity mode. Our results are obtained without using the rotating wave approximation (RWA), and the initial state (a dressed state) is easy to prepare. When the central frequency of the cavity mode is resonant with the qubit energy level spacing, the normalized decay rate of the qubit is lower than 1, which manifests the QZE. However, when the cavity frequency is detuned from resonance, the normalized decay rate becomes larger than 1, which corresponds to the AZE. The change from the QZE to the AZE, by just varying the central frequency of the cavity mode, should allow to distinguish these two different effects. Moreover, we find that in the presence of both qubit's intrinsic bath and the cavity bath, the emergence of the QZE and the AZE behaviors relies not only on the match between the qubit energy level spacing and the central frequency of the cavity mode, but also on the coupling strength between the qubit and the cavity mode.