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.
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.
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 quantum Zeno effect (QZE) is the striking possibility of inhibiting the decay of an unstable quantum state by sufficiently frequent measurements. This effect is currently believed to be universal, even though it has only been observed for oscillations between discrete states. Recently we showed that both the QZE and the inverse (anti-) Zeno effect (AZE) can be observed on spontaneous decay in cavities. We develop a general theory of evolution of quantum systems in the presence of frequent measurements. We consider both the ideal case of instantaneous projections of the wave function to the initial state and some possible measurement schemes. The considerations imply the impossibility of the continuous-observation limit necessary to stop quantum evolution (the quantum Zeno paradox). Indeed, this limit leads to an unbounded increase of the energy fluctuations of the system, which would cause the system to disintegrate. The present theory describes different measurement effects, including the QZE and AZE, and allows us to obtain the general criteria of their validity. In particular, we show that the AZE, rather than the QZE, is achievable for spontaneous decay of atoms in free space.
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.
It was predicted that frequently repeated measurements on an unstable state may alter the decay rate of the state. This is called the quantum Zeno effect (QZE) or the anti-Zeno effect (AZE), depending on whether the decay is suppressed or enhanced. In conventional theories of the QZE and AZE, effects of measurements are simply described by the projection postulate, assuming that each measurement is an instantaneous and ideal one. However, real measurements are not instantaneous and ideal. For the QZE and AZE by such general measurements, interesting and surprising features have recently been revealed, which we review in this article. The results are based on the quantum measurement theory, which is also reviewed briefly. As a typical model, we consider a continuous measurement of the decay of an excited atom by a photodetector that detects a photon emitted from the atom upon decay. This measurement is an indirect negative-result one, for which the curiosity of the QZE and AZE is emphasized. It is shown that the form factor is renormalized as a backaction of the measurement, through which the decay dynamics is modified. In a special case of the flat response, where the detector responds to every photon mode with an identical response time, results of the conventional theories are reproduced qualitatively. However, drastic differences emerge in general cases where the detector responds only to limited photon modes. For example, against predictions of the conventional theories, the QZE or AZE may take place even for states that exactly follow the exponential decay law. We also discuss relation to the cavity quantum electrodynamics.
Reiterated or continuous measurement on a quantum system impedes the quantum object's evolution. This "quantum Zeno" effect (QZE), contemplated for decades, has been conventionally attributed to the reaction of the measuring device on the quantum object being measured, in the sense of the Heisenberg microscope. However, even reactionless "quantum non-demolition" measurements seem to qualify for that inhibition to take place and may constitute a "quantum Zeno paradox" (QZP). An experimental proof of QZE had been attempted in the past on clouds of ions confined in a Paul trap. In the meantime it has been shown, however, that the anticipated impediment of the quantum evolution by a sheer gain of information, i.e. by reactionless measurement cannot be, in principle, proven with an ensemble. Recently, experiments have been performed with the use of a single quantum system: an 172Yb+ ion, laser-driven on its E2 line S1/2 - D5/2, or an 171Yb+ ion, microwave-driven on its ground-state hyperfine resonance. The results of these experiments demonstrate that mere gain of information on the quantum system, while lacking dynamic action, modifies the system's evolution as it is predicted by quantum mechanics, based on the system's preparation. This seems plausible if we attribute reality to the results of the measurements. If, in contrast, reality is claimed for the prediction, two-fold discontinuity must be admitted: loss of coherence with potential measurements, and renormalization from the results of actual measurements.