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To Catch and Reverse a Quantum Jump Mid-Flight (In Russian)

Zlatko Minev, Shantanu Mundhada, Shyam Shankar

Published Jul 1, 2019• 0 citations

Abstract

Quantum physics was invented to account for two fundamental features of measurement results their discreetness and randomness. Emblematic of these features is the Bohr idea of quantum jumps between two discrete energy levels of an atom. Experimentally, quantum jumps were first observed in an atomic ion driven by a weak deterministic force while under strong continuous energy measurement. The times at which the discontinuous jump transitions occur are reputed to be fundamentally unpredictable. Can there be, despite the indeterminism of quantum physics, a possibility to know if a quantum jump is about to occur or not? Here, we answer this question affirmatively by experimentally demonstrating that the jump from the ground to an excited state of a superconducting artificial three-level atom can be tracked as it follows a predictable flight, by monitoring the population of an auxiliary energy level coupled to the ground state. The experimental results demonstrate that the jump evolution when completed is continuous, coherent, and deterministic. Furthermore, exploiting these features and using real-time monitoring and feedback, we catch and reverse a quantum jump mid-flight, thus deterministically preventing its completion. Our results, which agree with theoretical predictions essentially without adjustable parameters, support the modern quantum trajectory theory and provide new ground for the exploration of real-time intervention techniques in the control of quantum systems, such as early detection of error syndromes.

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On catching and reversing a quantum jump mid-flight

Zlatko Minev, S.O. Mundhada, S. Shankar +6 more

We present results that experimentally demonstrate that the quantum jump from the ground state to an excited state of a superconducting artificial three-level atom can be tracked, caught, and reversed as it follows a predictable “flight.”

arXiv:1902.10355•The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting•Jan 1, 2019•14 citations

Quantum Jumps: Schrödinger’s Objections and the Contemporary Points of View

Sotirios A. Sakkopoulos

In 1913, when Bohr’s atom allowed electron jumps between discrete orbits, it was impossible to experiment on single atoms and study individually these jumps. Many people considered them not real, but something artificial for the explanation of the linear spectra of atoms. Especially Schrödinger rejected the image of negatively charged electrons orbiting around the nucleus and in particular their jumps from orbit to orbit. Finally, in 1986 single atoms (ions) laser cooled and confined in an electromagnetic trap gave the possibility to investigate experimentally electron jumps to and fro a metastable state. Recently, physicists experimenting on a macroscopic superconducting circuit with discrete quantum states analogous to a natural atom were able to halt and reverse quantum jumps mid-flight revealing very interesting details of them.

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Quantum Zeno Jumps in a Resonantly Driven Qubit under Frequent Measurements

In Nature, 570, 200 (2019), Minev and co-authors’ experiment shows how to deterministically “catch and reverse a quantum jump mid-flight” in a continuously-observed Rabi-stimulated qubit. Its interpretation is in debate (La Recherche, 555, 40, (2020)). We show that the quantum Zeno effect (QZE) of continuous measurement —by use of photon emission from a 3rd high-rate monitored ancilla level— can be described by an action-angle canonical transformation of the original Hamiltonian dynamical system (HDS) theory of QZE. Then energy whose mean value yields the well-known resonant Rabi harmonic dynamics is actually defined by large-amplitude high-frequency oscillations of the internal as well as of the overall phase of the two-level system. By making use of their standard deviation, we show that the separatrix crossing of the HDS trajectory yields the quantized action nh where n = 1, 2, 3 .... Therefore, the jump dynamics observed in Minev et al. experiment belongs to a series of discrete quantum jumps: it corresponds in this experiment to n = 3.

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A recent experiment by Minev et al., arXiv:1803.00545 demonstrated that in a dissipative (artificial) three-level atom with strongly intermittent dynamics it is possible to ``catch and reverse'' a quantum jump ``midflight'': by the conditional application of a unitary perturbation after a fixed time with no jumps, the system was prevented from getting shelved in the dark state, thus removing the intermittency from the dynamics. Here we offer an interpretation of this phenomenon in terms of the dynamical large deviation formalism for open quantum dynamics. In this approach, intermittency is seen as the first-order coexistence of active and inactive dynamical phases (or more precisely, dynamical regimes in this finite level system). Dark periods are thus like time bubbles of the inactive regime in the active one. Here we consider a controlled dynamics via the (single---as in the experiment---or multiple) application of a unitary control pulse during no-jump periods. By considering the large deviation statistics of the emissions, we show that appropriate choice of the control allows one to stabilize a desired dynamical regime and remove the intermittency. In the thermodynamic analogy, the effect of the control is to prick bubbles, thus preventing the fluctuations that manifest phase coexistence. We discuss similar controlled dynamics in broader settings.

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Feedback control in open quantum dynamics is crucial for the advancement of various coherent platforms. However, currently only a handful of feedback master equations exist in the literature, which are restricted to specific types of feedback. In this letter we first introduce a unifying framework, based on a single general equation, that describes all possible feedback schemes in sequentially (and continuously) measured systems, and from which all previous results follow. Next, we specialize it to the case of quantum jumps and introduce a new type of feedback based on the channel of the last detected jump, as well as the time elapsed since it occurred. Our description is experimentally grounded, and naturally allows for the introduction of realistic effects, such as time-delays in the feedback loop. We illustrate our results with two time-dependent feedback protocols conditioned on quantum-jump detections: one achieving population inversion of a two-level system against a thermal bath, and another enabling real-time reversal of quantum transitions, both admitting steady-state solutions.

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Timeless Approach to Quantum Jumps

Ignazio Francesco Licata, Leonardo Chiatti

According to the usual quantum description, the time evolution of the quantum state is continuous and deterministic except when a discontinuous and indeterministic collapse of state vector occurs. The collapse has been a central topic since the origin of the theory, although there are remarkable theoretical proposals to understand its nature, such as the Ghirardi–Rimini–Weber. Another possibility could be the assimilation of collapse with the now experimentally well established phenomenon of quantum jump, postulated by Bohr already in 1913. The challenge of nonlocality offers an opportunity to reconsider the quantum jump as a fundamental element of the logic of the physical world, rather than a subsidiary accident. We propose here a simple preliminary model that considers quantum jumps as processes of entry to and exit from the usual temporal domain to a timeless vacuum, without contradicting the quantum relativistic formalism, and we present some potential connections with particle physics. Quanta 2015; 4: 10–26.

Quanta•Oct 11, 2015•24 citations

Quantum physics was invented to account for two fundamental features of measurement results their discreetness and randomness. Emblematic of these features is the Bohr idea of quantum jumps between two discrete energy levels of an atom. Experimentally, quantum jumps were first observed in an atomic ion driven by a weak deterministic force while under strong continuous energy measurement. The times at which the discontinuous jump transitions occur are reputed to be fundamentally unpredictable. Can there be, despite the indeterminism of quantum physics, a possibility to know if a quantum jump is about to occur or not? Here, we answer this question affirmatively by experimentally demonstrating that the jump from the ground to an excited state of a superconducting artificial three-level atom can be tracked as it follows a predictable flight, by monitoring the population of an auxiliary energy level coupled to the ground state. The experimental results demonstrate that the jump evolution when completed is continuous, coherent, and deterministic. Furthermore, exploiting these features and using real-time monitoring and feedback, we catch and reverse a quantum jump mid-flight, thus deterministically preventing its completion. Our results, which agree with theoretical predictions essentially without adjustable parameters, support the modern quantum trajectory theory and provide new ground for the exploration of real-time intervention techniques in the control of quantum systems, such as early detection of error syndromes.

In 1913, when Bohr’s atom allowed electron jumps between discrete orbits, it was impossible to experiment on single atoms and study individually these jumps. Many people considered them not real, but something artificial for the explanation of the linear spectra of atoms. Especially Schrödinger rejected the image of negatively charged electrons orbiting around the nucleus and in particular their jumps from orbit to orbit. Finally, in 1986 single atoms (ions) laser cooled and confined in an electromagnetic trap gave the possibility to investigate experimentally electron jumps to and fro a metastable state. Recently, physicists experimenting on a macroscopic superconducting circuit with discrete quantum states analogous to a natural atom were able to halt and reverse quantum jumps mid-flight revealing very interesting details of them.

In Nature, 570, 200 (2019), Minev and co-authors’ experiment shows how to deterministically “catch and reverse a quantum jump mid-flight” in a continuously-observed Rabi-stimulated qubit. Its interpretation is in debate (La Recherche, 555, 40, (2020)). We show that the quantum Zeno effect (QZE) of continuous measurement —by use of photon emission from a 3rd high-rate monitored ancilla level— can be described by an action-angle canonical transformation of the original Hamiltonian dynamical system (HDS) theory of QZE. Then energy whose mean value yields the well-known resonant Rabi harmonic dynamics is actually defined by large-amplitude high-frequency oscillations of the internal as well as of the overall phase of the two-level system. By making use of their standard deviation, we show that the separatrix crossing of the HDS trajectory yields the quantized action nh where n = 1, 2, 3 .... Therefore, the jump dynamics observed in Minev et al. experiment belongs to a series of discrete quantum jumps: it corresponds in this experiment to n = 3.

A recent experiment by Minev et al., arXiv:1803.00545 demonstrated that in a dissipative (artificial) three-level atom with strongly intermittent dynamics it is possible to ``catch and reverse'' a quantum jump ``midflight'': by the conditional application of a unitary perturbation after a fixed time with no jumps, the system was prevented from getting shelved in the dark state, thus removing the intermittency from the dynamics. Here we offer an interpretation of this phenomenon in terms of the dynamical large deviation formalism for open quantum dynamics. In this approach, intermittency is seen as the first-order coexistence of active and inactive dynamical phases (or more precisely, dynamical regimes in this finite level system). Dark periods are thus like time bubbles of the inactive regime in the active one. Here we consider a controlled dynamics via the (single---as in the experiment---or multiple) application of a unitary control pulse during no-jump periods. By considering the large deviation statistics of the emissions, we show that appropriate choice of the control allows one to stabilize a desired dynamical regime and remove the intermittency. In the thermodynamic analogy, the effect of the control is to prick bubbles, thus preventing the fluctuations that manifest phase coexistence. We discuss similar controlled dynamics in broader settings.

Feedback control in open quantum dynamics is crucial for the advancement of various coherent platforms. However, currently only a handful of feedback master equations exist in the literature, which are restricted to specific types of feedback. In this letter we first introduce a unifying framework, based on a single general equation, that describes all possible feedback schemes in sequentially (and continuously) measured systems, and from which all previous results follow. Next, we specialize it to the case of quantum jumps and introduce a new type of feedback based on the channel of the last detected jump, as well as the time elapsed since it occurred. Our description is experimentally grounded, and naturally allows for the introduction of realistic effects, such as time-delays in the feedback loop. We illustrate our results with two time-dependent feedback protocols conditioned on quantum-jump detections: one achieving population inversion of a two-level system against a thermal bath, and another enabling real-time reversal of quantum transitions, both admitting steady-state solutions.

According to the usual quantum description, the time evolution of the quantum state is continuous and deterministic except when a discontinuous and indeterministic collapse of state vector occurs. The collapse has been a central topic since the origin of the theory, although there are remarkable theoretical proposals to understand its nature, such as the Ghirardi–Rimini–Weber. Another possibility could be the assimilation of collapse with the now experimentally well established phenomenon of quantum jump, postulated by Bohr already in 1913. The challenge of nonlocality offers an opportunity to reconsider the quantum jump as a fundamental element of the logic of the physical world, rather than a subsidiary accident. We propose here a simple preliminary model that considers quantum jumps as processes of entry to and exit from the usual temporal domain to a timeless vacuum, without contradicting the quantum relativistic formalism, and we present some potential connections with particle physics. Quanta 2015; 4: 10–26.