Weekly Papers on Quantum Foundations (22)

Authors: Krishan SaraswatNiayesh Afshordi

Two seemingly distinct notions regarding black holes have captured the imagination of theoretical physicists over the past decade: First, black holes are conjectured to be fast scramblers of information, a notion that is further supported through connections to quantum chaos and decay of mutual information via AdS/CFT holography. Second, black hole information paradox has motivated exotic quantum structure near horizons of black holes (e.g., gravastars, fuzzballs, or firewalls) that may manifest themselves through delayed gravitational wave echoes in the aftermath of black hole formation or mergers, and are potentially observable by LIGO/Virgo observatories. By studying various limits of charged AdS/Schwarzschild black holes we show that, if properly defined, the two seemingly distinct phenomena happen on an identical timescale of log(Radius)/$(\pi \times {\rm Temperature})$. We further comment on the physical interpretation of this coincidence and the corresponding holographic interpretation of black hole echoes.

Authors: Yuri G RudoyEnock O Oladimeji

In this paper the detailed investigation of one of the most interested models in the non relativistic quantum mechanics of one massive particle i.e., introduced by G. Poeschl and E. Teller in 1933 is presented. This model includes as particular cases two most popular and valuable models: the quasi free particle in the box with impenetrable hard walls (i.e., the model with confinement) and Bloch quantum harmonic oscillator, which is unconfined in space; both models are frequently and effectively exploited in modern nanotechnology e.g., in quantum dots and magnetic traps. We give the extensive and elementary exposition of the potentials, wave functions and energetic spectra of all these interconnected models. Moreover, the pressure operator is defined following the lines of G. Helmann and R. Feynman which were the first who introduced this idea in the late 30ies in quantum chemistry. By these means the baroenergetic equation of state is obtained and analyzed for all three models; in particular, it is shown the absence of the pressure for the Bloch oscillator due to the infinite width of the box. The generalization of these results on the case of nonzero temperature will be given later.

Authors: P. B. Lerner

The Gedankenexperiment advanced by Frauchiger and Renner in their Nature paper is based on an implicit assumption that one can synchronize stochastic measurement intervals between two non-interacting systems. This hypothesis, the author demonstrates, is equivalent to the complete entanglement of these systems. Consequently, Frauchiger and Renner’s postulate Q is too broad and, in general, meaningless. Accurate reformulation of the postulate, Q1 does not seem to entail any paradoxes with measurement. This paper is agnostic with respect to particular interpretations of quantum mechanics. Nor does it refer to the collapse of the wavefunction.

Authors: Steven B. Giddings

A succinct summary is given of the problem of reconciling observation of black hole-like objects with quantum mechanics. If quantum black holes behave like subsystems, and also decay, their information must be transferred to their environments. Interactions that accomplish this with `minimal’ departure from a standard description are parameterized. Possible sensitivity of gravitational wave or very long baseline interferometric observations to these interactions is briefly outlined.

Authors: A. HaririD. CuricL. GinerJ. S. Lundeen

The weak value, the average result of a weak measurement, has proven useful for probing quantum and classical systems. Examples include the amplification of small signals, investigating quantum paradoxes, and elucidating fundamental quantum phenomena such as geometric phase. A key characteristic of the weak value is that it can be complex, in contrast to a standard expectation value. However, typically only either the real or imaginary component of the weak value is determined in a given experimental setup. Weak measurements can be used to, in a sense, simultaneously measure non-commuting observables. This principle was used in the direct measurement of the quantum wavefunction. However, the wavefunction’s real and imaginary components, given by a weak value, are determined in different setups or on separate ensembles of systems, putting the procedure’s directness in question. To address these issues, we introduce and experimentally demonstrate a general method to simultaneously read out both components of the weak value in a single experimental apparatus. In particular, we directly measure the polarization state of an ensemble of photons using weak measurement. With our method, each photon contributes to both the real and imaginary parts of the weak-value average. On a fundamental level, this suggests that the full complex weak value is a characteristic of each photon measured.

In 1981, many of the world’s leading cosmologists gathered at the Pontifical Academy of Sciences, a vestige of the coupled lineages of science and theology located in an elegant villa in the gardens of the Vatican. Stephen Hawking chose the august setting to present what he would later regard as his most important idea: a proposal about how the universe could have arisen from nothing.

Before Hawking’s talk, all cosmological origin stories, scientific or theological, had invited the rejoinder, “What happened before that?” The Big Bang theory, for instance — pioneered 50 years before Hawking’s lecture by the Belgian physicist and Catholic priest Georges Lemaître, who later served as president of the Vatican’s academy of sciences — rewinds the expansion of the universe back to a hot, dense bundle of energy. But where did the initial energy come from?

The Big Bang theory had other problems. Physicists understood that an expanding bundle of energy would grow into a crumpled mess rather than the huge, smooth cosmos that modern astronomers observe. In 1980, the year before Hawking’s talk, the cosmologist Alan Guth realized that the Big Bang’s problems could be fixed with an add-on: an initial, exponential growth spurt known as cosmic inflation, which would have rendered the universe huge, smooth and flat before gravity had a chance to wreck it. Inflation quickly became the leading theory of our cosmic origins. Yet the issue of initial conditions remained: What was the source of the minuscule patch that allegedly ballooned into our cosmos, and of the potential energy that inflated it?

Hawking, in his brilliance, saw a way to end the interminable groping backward in time: He proposed that there’s no end, or beginning, at all. According to the record of the Vatican conference, the Cambridge physicist, then 39 and still able to speak with his own voice, told the crowd, “There ought to be something very special about the boundary conditions of the universe, and what can be more special than the condition that there is no boundary?”

The “no-boundary proposal,” which Hawking and his frequent collaborator, James Hartle, fully formulated in a 1983 paper, envisions the cosmos having the shape of a shuttlecock. Just as a shuttlecock has a diameter of zero at its bottommost point and gradually widens on the way up, the universe, according to the no-boundary proposal, smoothly expanded from a point of zero size. Hartle and Hawking derived a formula describing the whole shuttlecock — the so-called “wave function of the universe” that encompasses the entire past, present and future at once — making moot all contemplation of seeds of creation, a creator, or any transition from a time before.

“Asking what came before the Big Bang is meaningless, according to the no-boundary proposal, because there is no notion of time available to refer to,” Hawking said in another lecture at the Pontifical Academy in 2016, a year and a half before his death. “It would be like asking what lies south of the South Pole.”

Hartle and Hawking’s proposal radically reconceptualized time. Each moment in the universe becomes a cross-section of the shuttlecock; while we perceive the universe as expanding and evolving from one moment to the next, time really consists of correlations between the universe’s size in each cross-section and other properties — particularly its entropy, or disorder. Entropy increases from the cork to the feathers, aiming an emergent arrow of time. Near the shuttlecock’s rounded-off bottom, though, the correlations are less reliable; time ceases to exist and is replaced by pure space. As Hartle, now 79 and a professor at the University of California, Santa Barbara, explained it by phone recently, “We didn’t have birds in the very early universe; we have birds later on. … We didn’t have time in the early universe, but we have time later on.”

The no-boundary proposal has fascinated and inspired physicists for nearly four decades. “It’s a stunningly beautiful and provocative idea,” said Neil Turok, a cosmologist at the Perimeter Institute for Theoretical Physics in Waterloo, Canada, and a former collaborator of Hawking’s. The proposal represented a first guess at the quantum description of the cosmos — the wave function of the universe. Soon an entire field, quantum cosmology, sprang up as researchers devised alternative ideas about how the universe could have come from nothing, analyzed the theories’ various predictions and ways to test them, and interpreted their philosophical meaning. The no-boundary wave function, according to Hartle, “was in some ways the simplest possible proposal for that.”

But two years ago, a paper by Turok, Job Feldbrugge of the Perimeter Institute, and Jean-Luc Lehners of the Max Planck Institute for Gravitational Physics in Germany called the Hartle-Hawking proposal into question. The proposal is, of course, only viable if a universe that curves out of a dimensionless point in the way Hartle and Hawking imagined naturally grows into a universe like ours. Hawking and Hartle argued that indeed it would — that universes with no boundaries will tend to be huge, breathtakingly smooth, impressively flat, and expanding, just like the actual cosmos. “The trouble with Stephen and Jim’s approach is it was ambiguous,” Turok said — “deeply ambiguous.”

In their 2017 paper, published in Physical Review Letters, Turok and his co-authors approached Hartle and Hawking’s no-boundary proposal with new mathematical techniques that, in their view, make its predictions much more concrete than before. “We discovered that it just failed miserably,” Turok said. “It was just not possible quantum mechanically for a universe to start in the way they imagined.” The trio checked their math and queried their underlying assumptions before going public, but “unfortunately,” Turok said, “it just seemed to be inescapable that the Hartle-Hawking proposal was a disaster.”

The paper ignited a controversy. Other experts mounted a vigorous defense of the no-boundary idea and a rebuttal of Turok and colleagues’ reasoning. “We disagree with his technical arguments,” said Thomas Hertog, a physicist at the Catholic University of Leuven in Belgium who closely collaborated with Hawking for the last 20 years of the latter’s life. “But more fundamentally, we disagree also with his definition, his framework, his choice of principles. And that’s the more interesting discussion.”

After two years of sparring, the groups have traced their technical disagreement to differing beliefs about how nature works. The heated — yet friendly — debate has helped firm up the idea that most tickled Hawking’s fancy. Even critics of his and Hartle’s specific formula, including Turok and Lehners, are crafting competing quantum-cosmological models that try to avoid the alleged pitfalls of the original while maintaining its boundless allure.

Garden of Cosmic Delights

Hartle and Hawking saw a lot of each other from the 1970s on, typically when they met in Cambridge for long periods of collaboration. The duo’s theoretical investigations of black holes and the mysterious singularities at their centers had turned them on to the question of our cosmic origin.

In 1915, Albert Einstein discovered that concentrations of matter or energy warp the fabric of space-time, causing gravity. In the 1960s, Hawking and the Oxford University physicist Roger Penrose proved that when space-time bends steeply enough, such as inside a black hole or perhaps during the Big Bang, it inevitably collapses, curving infinitely steeply toward a singularity, where Einstein’s equations break down and a new, quantum theory of gravity is needed. The Penrose-Hawking “singularity theorems” meant there was no way for space-time to begin smoothly, undramatically at a point.

Hawking and Hartle were thus led to ponder the possibility that the universe began as pure space, rather than dynamical space-time. And this led them to the shuttlecock geometry. They defined the no-boundary wave function describing such a universe using an approach invented by Hawking’s hero, the physicist Richard Feynman. In the 1940s, Feynman devised a scheme for calculating the most likely outcomes of quantum mechanical events. To predict, say, the likeliest outcomes of a particle collision, Feynman found that you could sum up all possible paths that the colliding particles could take, weighting straightforward paths more than convoluted ones in the sum. Calculating this “path integral” gives you the wave function: a probability distribution indicating the different possible states of the particles after the collision.

Likewise, Hartle and Hawking expressed the wave function of the universe — which describes its likely states — as the sum of all possible ways that it might have smoothly expanded from a point. The hope was that the sum of all possible “expansion histories,” smooth-bottomed universes of all different shapes and sizes, would yield a wave function that gives a high probability to a huge, smooth, flat universe like ours. If the weighted sum of all possible expansion histories yields some other kind of universe as the likeliest outcome, the no-boundary proposal fails.

The problem is that the path integral over all possible expansion histories is far too complicated to calculate exactly. Countless different shapes and sizes of universes are possible, and each can be a messy affair. “Murray Gell-Mann used to ask me,” Hartle said, referring to the late Nobel Prize-winning physicist, “if you know the wave function of the universe, why aren’t you rich?” Of course, to actually solve for the wave function using Feynman’s method, Hartle and Hawking had to drastically simplify the situation, ignoring even the specific particles that populate our world (which meant their formula was nowhere close to being able to predict the stock market). They considered the path integral over all possible toy universes in “minisuperspace,” defined as the set of all universes with a single energy field coursing through them: the energy that powered cosmic inflation. (In Hartle and Hawking’s shuttlecock picture, that initial period of ballooning corresponds to the rapid increase in diameter near the bottom of the cork.)

Even the minisuperspace calculation is hard to solve exactly, but physicists know there are two possible expansion histories that potentially dominate the calculation. These rival universe shapes anchor the two sides of the current debate.

The rival solutions are the two “classical” expansion histories that a universe can have. Following an initial spurt of cosmic inflation from size zero, these universes steadily expand according to Einstein’s theory of gravity and space-time. Weirder expansion histories, like football-shaped universes or caterpillar-like ones, mostly cancel out in the quantum calculation.

One of the two classical solutions resembles our universe. On large scales, it’s smooth and randomly dappled with energy, due to quantum fluctuations during inflation. As in the real universe, density differences between regions form a bell curve around zero. If this possible solution does indeed dominate the wave function for minisuperspace, it becomes plausible to imagine that a far more detailed and exact version of the no-boundary wave function might serve as a viable cosmological model of the real universe.

The other potentially dominant universe shape is nothing like reality. As it widens, the energy infusing it varies more and more extremely, creating enormous density differences from one place to the next that gravity steadily worsens. Density variations form an inverted bell curve, where differences between regions approach not zero, but infinity. If this is the dominant term in the no-boundary wave function for minisuperspace, then the Hartle-Hawking proposal would seem to be wrong.

The two dominant expansion histories present a choice in how the path integral should be done. If the dominant histories are two locations on a map, megacities in the realm of all possible quantum mechanical universes, the question is which path we should take through the terrain. Which dominant expansion history, and there can only be one, should our “contour of integration” pick up? Researchers have forked down different paths.

In their 2017 paper, Turok, Feldbrugge and Lehners took a path through the garden of possible expansion histories that led to the second dominant solution. In their view, the only sensible contour is one that scans through real values (as opposed to imaginary values, which involve the square roots of negative numbers) for a variable called “lapse.” Lapse is essentially the height of each possible shuttlecock universe — the distance it takes to reach a certain diameter. Lacking a causal element, lapse is not quite our usual notion of time. Yet Turok and colleagues argue partly on the grounds of causality that only real values of lapse make physical sense. And summing over universes with real values of lapse leads to the wildly fluctuating, physically nonsensical solution.

“People place huge faith in Stephen’s intuition,” Turok said by phone. “For good reason — I mean, he probably had the best intuition of anyone on these topics. But he wasn’t always right.”

Imaginary Universes

Jonathan Halliwell, a physicist at Imperial College London, has studied the no-boundary proposal since he was Hawking’s student in the 1980s. He and Hartle analyzed the issue of the contour of integration in 1990. In their view, as well as Hertog’s, and apparently Hawking’s, the contour is not fundamental, but rather a mathematical tool that can be placed to greatest advantage. It’s similar to how the trajectory of a planet around the sun can be expressed mathematically as a series of angles, as a series of times, or in terms of any of several other convenient parameters. “You can do that parameterization in many different ways, but none of them are any more physical than another one,” Halliwell said.

He and his colleagues argue that, in the minisuperspace case, only contours that pick up the good expansion history make sense. Quantum mechanics requires probabilities to add to 1, or be “normalizable,” but the wildly fluctuating universe that Turok’s team landed on is not. That solution is nonsensical, plagued by infinities and disallowed by quantum laws — obvious signs, according to no-boundary’s defenders, to walk the other way.

It’s true that contours passing through the good solution sum up possible universes with imaginary values for their lapse variables. But apart from Turok and company, few people think that’s a problem. Imaginary numbers pervade quantum mechanics. To team Hartle-Hawking, the critics are invoking a false notion of causality in demanding that lapse be real. “That’s a principle which is not written in the stars, and which we profoundly disagree with,” Hertog said.

According to Hertog, Hawking seldom mentioned the path integral formulation of the no-boundary wave function in his later years, partly because of the ambiguity around the choice of contour. He regarded the normalizable expansion history, which the path integral had merely helped uncover, as the solution to a more fundamental equation about the universe posed in the 1960s by the physicists John Wheeler and Bryce DeWitt. Wheeler and DeWitt — after mulling over the issue during a layover at Raleigh-Durham International — argued that the wave function of the universe, whatever it is, cannot depend on time, since there is no external clock by which to measure it. And thus the amount of energy in the universe, when you add up the positive and negative contributions of matter and gravity, must stay at zero forever. The no-boundary wave function satisfies the Wheeler-DeWitt equation for minisuperspace.  

In the final years of his life, to better understand the wave function more generally, Hawking and his collaborators started applying holography — a blockbuster new approach that treats space-time as a hologram. Hawking sought a holographic description of a shuttlecock-shaped universe, in which the geometry of the entire past would project off of the present.

That effort is continuing in Hawking’s absence. But Turok sees this shift in emphasis as changing the rules. In backing away from the path integral formulation, he says, proponents of the no-boundary idea have made it ill-defined. What they’re studying is no longer Hartle-Hawking, in his opinion — though Hartle himself disagrees.

For the past year, Turok and his Perimeter Institute colleagues Latham Boyle and Kieran Finn have been developing a new cosmological model that has much in common with the no-boundary proposal. But instead of one shuttlecock, it envisions two, arranged cork to cork in a sort of hourglass figure with time flowing in both directions. While the model is not yet developed enough to make predictions, its charm lies in the way its lobes realize CPT symmetry, a seemingly fundamental mirror in nature that simultaneously reflects matter and antimatter, left and right, and forward and backward in time. One disadvantage is that the universe’s mirror-image lobes meet at a singularity, a pinch in space-time that requires the unknown quantum theory of gravity to understand. Boyle, Finn and Turok take a stab at the singularity, but such an attempt is inherently speculative.

There has also been a revival of interest in the “tunneling proposal,” an alternative way that the universe might have arisen from nothing, conceived in the ’80s independently by the Russian-American cosmologists Alexander Vilenkin and Andrei Linde. The proposal, which differs from the no-boundary wave function primarily by way of a minus sign, casts the birth of the universe as a quantum mechanical “tunneling” event, similar to when a particle pops up beyond a barrier in a quantum mechanical experiment.

Questions abound about how the various proposals intersect with anthropic reasoning and the infamous multiverse idea. The no-boundary wave function, for instance, favors empty universes, whereas significant matter and energy are needed to power hugeness and complexity. Hawking argued that the vast spread of possible universes permitted by the wave function must all be realized in some larger multiverse, within which only complex universes like ours will have inhabitants capable of making observations. (The recent debate concerns whether these complex, habitable universes will be smooth or wildly fluctuating.) An advantage of the tunneling proposal is that it favors matter- and energy-filled universes like ours without resorting to anthropic reasoning — though universes that tunnel into existence may have other problems.

No matter how things go, perhaps we’ll be left with some essence of the picture Hawking first painted at the Pontifical Academy of Sciences 38 years ago. Or perhaps, instead of a South Pole-like non-beginning, the universe emerged from a singularity after all, demanding a different kind of wave function altogether. Either way, the pursuit will continue. “If we are talking about a quantum mechanical theory, what else is there to find other than the wave function?” asked Juan Maldacena, an eminent theoretical physicist at the Institute for Advanced Study in Princeton, New Jersey, who has mostly stayed out of the recent fray. The question of the wave function of the universe “is the right kind of question to ask,” said Maldacena, who, incidentally, is a member of the Pontifical Academy. “Whether we are finding the right wave function, or how we should think about the wave function — it’s less clear.”

Correction: This article was revised on June 6, 2019, to list Latham Boyle and Kieran Finn as co-developers of the CPT-symmetric universe idea.

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When quantum mechanics was first developed a century ago as a theory for understanding the atomic-scale world, one of its key concepts was so radical, bold and counter-intuitive that it passed into popular language: the “quantum leap.” Purists might object that the common habit of applying this term to a big change misses the point that jumps between two quantum states are typically tiny, which is precisely why they weren’t noticed sooner. But the real point is that they’re sudden. So sudden, in fact, that many of the pioneers of quantum mechanics assumed they were instantaneous.

A new experiment shows that they aren’t. By making a kind of high-speed movie of a quantum leap, the work reveals that the process is as gradual as the melting of a snowman in the sun. “If we can measure a quantum jump fast and efficiently enough,” said Michel Devoret of Yale University, “it is actually a continuous process.” The study, which was led by Zlatko Minev, a graduate student in Devoret’s lab, was published on Monday in Nature. Already, colleagues are excited. “This is really a fantastic experiment,” said the physicist William Oliver of the Massachusetts Institute of Technology, who wasn’t involved in the work. “Really amazing.”

But there’s more. With their high-speed monitoring system, the researchers could spot when a quantum jump was about to appear, “catch” it halfway through, and reverse it, sending the system back to the state in which it started. In this way, what seemed to the quantum pioneers to be unavoidable randomness in the physical world is now shown to be amenable to control. We can take charge of the quantum.

All Too Random

The abruptness of quantum jumps was a central pillar of the way quantum theory was formulated by Niels Bohr, Werner Heisenberg and their colleagues in the mid-1920s, in a picture now commonly called the Copenhagen interpretation. Bohr had argued earlier that the energy states of electrons in atoms are “quantized”: Only certain energies are available to them, while all those in between are forbidden. He proposed that electrons change their energy by absorbing or emitting quantum particles of light — photons — that have energies matching the gap between permitted electron states. This explained why atoms and molecules absorb and emit very characteristic wavelengths of light — why many copper salts are blue, say, and sodium lamps yellow.

Bohr and Heisenberg began to develop a mathematical theory of these quantum phenomena in the 1920s. Heisenberg’s quantum mechanics enumerated all the allowed quantum states, and implicitly assumed that jumps between them are instant — discontinuous, as mathematicians would say. “The notion of instantaneous quantum jumps … became a foundational notion in the Copenhagen interpretation,” historian of science Mara Beller has written.

Another of the architects of quantum mechanics, the Austrian physicist Erwin Schrödinger, hated that idea. He devised what seemed at first to be an alternative to Heisenberg’s math of discrete quantum states and instant jumps between them. Schrödinger’s theory represented quantum particles in terms of wavelike entities called wave functions, which changed only smoothly and continuously over time, like gentle undulations on the open sea. Things in the real world don’t switch suddenly, in zero time, Schrödinger thought — discontinuous “quantum jumps” were just a figment of the mind. In a 1952 paper called “Are there quantum jumps?,” Schrödinger answered with a firm “no,” his irritation all too evident in the way he called them “quantum jerks.”

The argument wasn’t just about Schrödinger’s discomfort with sudden change. The problem with a quantum jump was also that it was said to just happen at a random moment — with nothing to say why that particular moment. It was thus an effect without a cause, an instance of apparent randomness inserted into the heart of nature. Schrödinger and his close friend Albert Einstein could not accept that chance and unpredictability reigned at the most fundamental level of reality. According to the German physicist Max Born, the whole controversy was therefore “not so much an internal matter of physics, as one of its relation to philosophy and human knowledge in general.” In other words, there’s a lot riding on the reality (or not) of quantum jumps.

Seeing Without Looking

To probe further, we need to see quantum jumps one at a time. In 1986, three teams of researchers reportedthem happening in individual atoms suspended in space by electromagnetic fields. The atoms flipped between a “bright” state, where they could emit a photon of light, and a “dark” state that did not emit at random moments, remaining in one state or the other for periods of between a few tenths of a second and a few seconds before jumping again. Since then, such jumps have been seen in various systems, ranging from photons switching between quantum states to atoms in solid materials jumping between quantized magnetic states. In 2007 a team in France reported jumps that correspond to what they called “the birth, life and death of individual photons.”

In these experiments the jumps indeed looked abrupt and random — there was no telling, as the quantum system was monitored, when they would happen, nor any detailed picture of what a jump looked like. The Yale team’s setup, by contrast, allowed them to anticipate when a jump was coming, then zoom in close to examine it. The key to the experiment is the ability to collect just about all of the available information about it, so that none leaks away into the environment before it can be measured. Only then can they follow single jumps in such detail.

The quantum systems the researchers used are much larger than atoms, consisting of wires made from a superconducting material — sometimes called “artificial atoms” because they have discrete quantum energy states analogous to the electron states in real atoms. Jumps between the energy states can be induced by absorbing or emitting a photon, just as they are for electrons in atoms.

Devoret and colleagues wanted to watch a single artificial atom jump between its lowest-energy (ground) state and an energetically excited state. But they couldn’t monitor that transition directly, because making a measurement on a quantum system destroys the coherence of the wave function — its smooth wavelike behavior  — on which quantum behavior depends. To watch the quantum jump, the researchers had to retain this coherence. Otherwise they’d “collapse” the wave function, which would place the artificial atom in one state or the other. This is the problem famously exemplified by Schrödinger’s cat, which is allegedly placed in a coherent quantum “superposition” of live and dead states but becomes only one or the other when observed.

To get around this problem, Devoret and colleagues employ a clever trick involving a second excited state. The system can reach this second state from the ground state by absorbing a photon of a different energy. The researchers probe the system in a way that only ever tells them whether the system is in this second “bright” state, so named because it’s the one that can be seen. The state to and from which the researchers are actually looking for quantum jumps is, meanwhile, the “dark” state — because it remains hidden from direct view.

The researchers placed the superconducting circuit in an optical cavity (a chamber in which photons of the right wavelength can bounce around) so that, if the system is in the bright state, the way that light scatters in the cavity changes. Every time the bright state decays by emission of a photon, the detector gives off a signal akin to a Geiger counter’s “click.”

The key here, said Oliver, is that the measurement provides information about the state of the system without interrogating that state directly. In effect, it asks whether the system is in, or is not in, the ground and dark states collectively. That ambiguity is crucial for maintaining quantum coherence during a jump between these two states. In this respect, said Oliver, the scheme that the Yale team has used is closely related to those employed for error correction in quantum computers. There, too, it’s necessary to get information about quantum bits without destroying the coherence on which the quantum computation relies. Again, this is done by not looking directly at the quantum bit in question but probing an auxiliary state coupled to it.

The strategy reveals that quantum measurement is not about the physical perturbation induced by the probe but about what you know (and what you leave unknown) as a result. “Absence of an event can bring as much information as its presence,” said Devoret. He compares it to the Sherlock Holmes story in which the detective infers a vital clue from the “curious incident” in which a dog did not do anything in the night. Borrowing from a different (but often confused) dog-related Holmes story, Devoret calls it “Baskerville’s Hound meets Schrödinger’s Cat.”

To Catch a Jump

The Yale team saw a series of clicks from the detector, each signifying a decay of the bright state, arriving typically every few microseconds. This stream of clicks was interrupted approximately every few hundred microseconds, apparently at random, by a hiatus in which there were no clicks. Then after a period of typically 100 microseconds or so, the clicks resumed. During that silent time, the system had presumably undergone a transition to the dark state, since that’s the only thing that can prevent flipping back and forth between the ground and bright states.

So here in these switches from “click” to “no-click” states are the individual quantum jumps — just like those seen in the earlier experiments on trapped atoms and the like. However, in this case Devoret and colleagues could see something new.

Before each jump to the dark state, there would typically be a short spell where the clicks seemed suspended: a pause that acted as a harbinger of the impending jump. “As soon as the length of a no-click period significantly exceeds the typical time between two clicks, you have a pretty good warning that the jump is about to occur,” said Devoret.

That warning allowed the researchers to study the jump in greater detail. When they saw this brief pause, they switched off the input of photons driving the transitions. Surprisingly, the transition to the dark state still happened even without photons driving it — it is as if, by the time the brief pause sets in, the fate is already fixed. So although the jump itself comes at a random time, there is also something deterministic in its approach.

With the photons turned off, the researchers zoomed in on the jump with fine-grained time resolution to see it unfold. Does it happen instantaneously — the sudden quantum jump of Bohr and Heisenberg? Or does it happen smoothly, as Schrödinger insisted it must? And if so, how?

The team found that jumps are in fact gradual. That’s because, even though a direct observation could reveal the system only as being in one state or another, during a quantum jump the system is in a superposition, or mixture, of these two end states. As the jump progresses, a direct measurement would be increasingly likely to yield the final rather than the initial state. It’s a bit like the way our decisions may evolve over time. You can only either stay at a party or leave it — it’s a binary choice — but as the evening wears on and you get tired, the question “Are you staying or leaving?” becomes increasingly likely to get the answer “I’m leaving.”

The techniques developed by the Yale team reveal the changing mindset of a system during a quantum jump. Using a method called tomographic reconstruction, the researchers could figure out the relative weightings of the dark and ground states in the superposition. They saw these weights change gradually over a period of a few microseconds. That’s pretty fast, but it’s certainly not instantaneous.

What’s more, this electronic system is so fast that the researchers could “catch” the switch between the two states as it is happening, then reverse it by sending a pulse of photons into the cavity to boost the system back to the dark state. They can persuade the system to change its mind and stay at the party after all.

Flash of Insight

The experiment shows that quantum jumps “are indeed not instantaneous if we look closely enough,” said Oliver, “but are coherent processes”: real physical events that unfold over time.

The gradualness of the “jump” is just what is predicted by a form of quantum theory called quantum trajectories theory, which can describe individual events like this. “It is reassuring that the theory matches perfectly with what is seen” said David DiVincenzo, an expert in quantum information at Aachen University in Germany, “but it’s a subtle theory, and we are far from having gotten our heads completely around it.”

The possibility of predicting a quantum jumps just before they occur, said Devoret, makes them somewhat like volcanic eruptions. Each eruption happens unpredictably, but some big ones can be anticipated by watching for the atypically quiet period that precedes them. “To the best of our knowledge, this precursory signal has not been proposed or measured before,” he said.

Devoret said that an ability to spot precursors to quantum jumps might find applications in quantum sensing technologies. For example, “in atomic clock measurements, one wants to synchronize the clock to the transition frequency of an atom, which serves as a reference,” he said. But if you can detect right at the start if the transition is about to happen, rather than having to wait for it to be completed, the synchronization can be faster and therefore more precise in the long run.

DiVincenzo thinks that the work might also find applications in error correction for quantum computing, although he sees that as “quite far down the line.” To achieve the level of control needed for dealing with such errors, though, will require this kind of exhaustive harvesting of measurement data — rather like the data-intensive situation in particle physics, said DiVincenzo.

The real value of the result is not, though, in any practical benefits; it’s a matter of what we learn about the workings of the quantum world. Yes, it is shot through with randomness — but no, it is not punctuated by instantaneous jerks. Schrödinger, aptly enough, was both right and wrong at the same time.

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Gryb, Sean and Palacios, Patricia and Thebault, Karim P Y (2019) On the Universality of Hawking Radiation. [Preprint]
Making a Difference: Essays on the Philosophy of Causation Edited by BeebeeHelen, HitchcockChristopher and PriceHuwOxford University Press, 2017. xii + 336 pp.

Nature, Published online: 03 June 2019; doi:10.1038/s41586-019-1287-z

Experiment overturns Bohr’s view of quantum jumps, demonstrating that they possess a degree of predictability and when completed are continuous, coherent and even deterministic.

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