Magdalena Zych

Universal decoherence due to gravitational time dilation

Gravity and quantum mechanics are expected to meet at extreme energy scales, but time dilation could induce decoherence even at low energies affecting microscopic objects—a prospect that could be tested in future matter-wave experiments.

Generalization of the Margolus-Levitin bound

The Margolus-Levitin lower bound on the minimal time required for a state to be transformed into an orthogonal state is generalized. It is shown that for some initial states the new bound is stronger than the Margolus-Levitin one.

Quantum test of the equivalence principle for atoms in coherent superposition of internal energy states

The Einstein equivalence principle (EEP) has a central role in the understanding of gravity and space–time. In its weak form, or weak equivalence principle (WEP), it directly implies equivalence between inertial and gravitational mass. Verifying this principle in a regime where the relevant properties of the test body must be described by quantum theory has profound implications. Here we report on a novel WEP test for atoms: a Bragg atom interferometer in a gravity gradiometer configuration compares the free fall of rubidium atoms prepared in two hyperfine states and in their coherent superposition. The use of the superposition state allows testing genuine quantum aspects of EEP with no classical analogue, which have remained completely unexplored so far. In addition, we measure the Eötvös ratio of atoms in two hyperfine levels with relative uncertainty in the low 10−9, improving previous results by almost two orders of magnitude.

General relativistic effects in quantum interference of photons

Quantum mechanics and general relativity have been extensively and independently confirmed in many experiments. However, the interplay of the two theories has never been tested: all experiments that measured the influence of gravity on quantum systems are consistent with non-relativistic, Newtonian gravity. On the other hand, all tests of general relativity can be described within the framework of classical physics. Here we discuss a quantum interference experiment with single photons that can probe quantum mechanics in curved space-time. We consider a single photon traveling in superposition along two paths in an interferometer, with each arm experiencing a different gravitational time dilation. If the difference in the time dilations is comparable with the photon’s coherence time, the visibility of the quantum interference is predicted to drop, while for shorter time dilations the effect of gravity will result only in a relative phase shift between the two arms. We discuss what aspects of the interplay between quantum mechanics and general relativity are probed in such experiments and analyze the experimental feasibility.

Quantum Formulation of the Einstein Equivalence Principle

Results of the previous chapters rely on the validity of both quantum theory and classical general relativity. However, in order to ensure that gravity indeed can be described in terms of a space-time metric, as in general relativity, dynamics of physical systems has to satisfy certain conditions. These conditions comprise the Einstein Equivalence Principle (EEP). This chapter analyses the EEP for quantum systems. The results show that validity of the metric picture of gravity in classical physics does not imply its validity in quantum mechanics. Very generally, quantised interactions bring in new physical effects, not present in the classical limit, which in turn implies that testing the structure of quantised dynamics is more requiring—conceptually new test are necessary and more parameters need to be constrained.

Unitarity, feedback, interactions—dynamics emergent from repeated measurements

Motivated by the recent efforts to describe the gravitational interaction as a classical channel arising from continuous quantum measurements, we study what types of dynamics can emerge from a collisional model of repeated interactions between a system and a set of ancillae. We show that contingent on the model parameters the resulting dynamics ranges from exact unitarity to arbitrarily fast decoherence (quantum Zeno effect). For a series of measurements the effective dynamics includes feedback-control, which for a composite system yields effective interactions between the subsystems. We quantify the amount of decoherence accompanying such induced interactions, generalizing the lower bound found for the gravitational example. However, by allowing multipartite measurements, we show that interactions can be induced with arbitrarily low decoherence. These results have implications for gravity-inspired decoherence models. Moreover, we show how the framework can include terms beyond the usual second-order approximation, which can spark new quantum control or simulation protocols. Finally, within our simple approach we re-derive the quantum filtering equations for the different regimes of effective dynamics, which can facilitate new connections between different formulations of open systems.

Entanglement between smeared field operators in the Klein-Gordon vacuum

Quantum field theory is the application of quantum physics to fields. It provides a theoretical framework widely used in particle physics and condensed matter physics. One of the most distinct features of quantum physics with respect to classical physics is entanglement or the existence of strong correlations between subsystems that can even be spacelike separated. In quantum fields, observables restricted to a region of space define a subsystem. While there are proofs on the existence of local observables that would allow a violation of Bells inequalities in the vacuum states of quantum fields as well as some explicit but technically demanding schemes requiring an extreme fine-tuning of the interaction between the fields and detectors, an experimentally accessible entanglement witness for quantum fields is still missing. Here we introduce smeared field operators which allow reducing the vacuum to a system of two effective bosonic modes. The introduction of such collective observables is motivated by the fact that no physical probe has access to fields in single spatial (mathematical) points but rather smeared over finite volumes. We first give explicit collective observables whose correlations reveal vacuum entanglement in the Klein-Gordon field. We then show that the critical distance between the two regions of space above which two effective bosonic modes become separable is of the order of the Compton wavelength of the particle corresponding to the massive Klein-Gordon field.

Gravity is not a Pairwise Local Classical Channel

It is currently believed that there is no experimental evidence on possibly quantum features of gravity or gravity-motivated modifications of quantum mechanics. Here we show that single-atom interference experi- ments achieving large spatial superpositions can rule out a framework where the Newtonian gravitational inter- action is fundamentally classical in the information-theoretic sense: it cannot convey entanglement. Specifically, in this framework gravity acts pairwise between massive particles as classical channels, which effectively induce approximately Newtonian forces between the masses. The experiments indicate that if gravity does reduce to the pairwise Newtonian interaction between atoms at the low energies, this interaction cannot arise from the exchange of just classical information, and in principle has the capacity to create entanglement. We clarify that, contrary to current belief, the classical-channel description of gravity differs from the model of Diosi and Penrose, which is not constrained by the same data.

Single electron relativistic clock interferometer

Although time is one of the fundamental notions in physics, it does not have a unique description. In quantum theory time is a parameter ordering the succession of the probability amplitudes of a quantum system, while according to relativity theory each system experiences in general a different proper time, depending on the systems world line, due to time to time dilation. It is therefore of fundamental interest to test the notion of time in the regime where both quantum and relativistic effects play a role, for example, when different amplitudes of a single quantum clock experience different magnitudes of time dilation. Here we propose a realization of such an experiment with a single electron in a Penning trap. The clock can be implemented in the electronic spin precession and its time dilation then depends on the radial (cyclotron) state of the electron. We show that coherent manipulation and detection of the electron can be achieved already with present day technology. A single electron in a Penning trap is a technologically ready platform where the notion of time can be probed in a hitherto untested regime, where it requires a relativistic as well as quantum description.

Decoherence from Time Dilation

This chapter generalises the discussion of time dilation effects on “clocks”—quantum systems whose internal states are pure and time evolving (Chap. 5)—to systems in an arbitrary internal state.