In most imaging experiments, the structure of an object is defined in a position space. Such a structural pattern can be stationary, or for a dynamic object it can be nonstationary with time. An image of such an optically responsive object can be produced with a lens, therefore such an object can be seen with a camera or by the human eye. In this paper, we go beyond the conventional notion of imaging. A structural pattern of objects in our experiment is defined in a phase space, therefore such a pattern cannot be imaged with a lens or a camera, and the human eye cannot visualize it. A pattern in phase space is produced from object transparencies and imprinted onto the phase space of an atomic gaseous medium of a Doppler-broadened absorption profile at room temperature by utilizing velocity-selective hole burning in the absorption profile. The pattern is localized in a unique three-dimensional phase space, which is a subspace of the six-dimensional phase space. Tomographic images of the localized phase-space pattern are captured at different momentum locations by a laser light that has never interacted with actual objects. In addition, imaging of an imprinted phase-space pattern of an object of nonuniform transmittance is presented.

Multiphoton quantum interference underpins fundamental tests of quantum mechanics and quantum technologies. Consequently, the detrimental effect of photon distinguishability in multiphoton interference experiments can be catastrophic. Here we employ correlation measurements in the photonic inner modes, time or frequency, to restore quantum interference between photons differing in their colors or injection times in arbitrary linear optical networks, without the need for additional filtering or postselection. Interestingly, we demonstrate how harnessing the multiphoton inner-mode quantum information enables us to infer information about symmetries of multiphoton networks and states and to observe arbitrary degrees of $W$-state entanglement between a small number of photons with a fixed interferometer. These results are therefore of profound interest for future applications of universal inner-mode-resolved linear optics across fundamental science and quantum technologies with photons with experimentally different spectral properties.

Using an entanglement-preserving approach, we theoretically study the reservoir-induced photonic dissipations in waveguide quantum electrodynamic (wQED) systems coupled to an excitable reservoir consisting of oscillators. For the single-photon case, we show that the effects of dissipation can be described by a reduced Hamiltonian and a restricted eigenstate. For the multiphoton case, we show that the reduced Hamiltonian approach is, in general, not valid. Nonetheless, we identify a weak-reservoir condition for the reduced Hamiltonian approach to be approximately valid, which applies to the majority of current experiments. In addition, we apply the density matrix approach to investigate the same physical system and show that the Markovian density matrix approach can describe only the lowest-order dissipative effect. The deviations from the weak-reservoir scenario are suggested to be observable in an engineered excitable reservoir consisting of optical cavities.

We report on optical levitation experiments to probe the interaction of a nanoparticle with a surface in vacuum. The observed interaction-induced effect is a controllable anharmonicity of the particle trapping potential. We reconstruct the Coulomb image charge interaction potential to be in perfect agreement with the experimental data for a particle carrying $Q=-(11\pm 1)e$ elementary charges and compare the measured electrostatic interaction with the weaker dispersive forces from theory. Our experimental results may open the route for a new surface sensitive scanning probe technique based on the high mechanical sensitivity of levitated nanoparticles.

Enhanced sensitivity in electromagnetically induced transparency (EIT) can be obtained by the use of noise correlation spectroscopy between the fields involved in the process. Here, we investigate EIT in a cold ($<1$ mK) rubidium vapor and demonstrate sensitivity to detect weak light-induced forces on the atoms. A theoretical model is developed and shows good agreement with our measurements, enabling the attribution of the observed effects to the coupling of the atomic states to their motion. The effects remain unnoticed on the measurement of the mean fields but are clearly manifest in their correlations.

We employ a trapped ion to study quantum contextual correlations in a single qutrit using the 5-observable Klyachko, Can, Binicioğlu, and Shumovsky inequality, which is arguably the most fundamental noncontextuality inequality for testing quantum mechanics (QM). We quantify the effect of systematics in our experiment by purposely scanning the degree of signaling between measurements, which allows us to place realistic bounds on the nonclassicality of the observed correlations. Our results violate the classical bound for this experiment by up to 25 standard deviations, while being in agreement with the QM limit. In order to test the prediction of QM that the contextual fraction increases with the number of observables, we gradually increase the complexity of our measurements from 5 up to 121 observables. We find stronger-than-classical correlations in all prepared scenarios up to 101 observables, beyond which experimental imperfections blur the quantum-classical divide.

Dynamics of an electron beam head-on colliding with an ultraintense focused ultrashort circularly polarized laser pulse are investigated in the quantum radiation-dominated regime. Generally, the ponderomotive force of the laser fields may deflect the electrons transversely, to form a ring structure in the cross section of the electron beam. However, we find that when the Lorentz factor of the electron $\gamma$ is approximately one order of magnitude larger than the invariant laser field parameter $\xi$, the stochastic nature of the photon emission leads to electron aggregation abnormally inwards to the propagation axis of the laser pulse. Consequently, the electron angular distribution after the interaction exhibits a peak structure in the beam propagation direction, which is noticeably distinguished from the “ring” structure of the distribution in the classical regime and, therefore, can be recognized as a proof of the fundamental quantum stochastic nature of radiation. The stochasticity signature is robust with respect to the laser and electron parameters and observable with current experimental techniques.

Models of spontaneous wave function collapse predict a small heating rate for a bulk solid, as a result of coupling to the noise field that causes collapse. This rate is small enough that ambient radioactivity and cosmic ray flux on the surface of the earth can mask the heating due to spontaneous collapse. In this paper we estimate the background noise due to $\gamma$ radiation and cosmic ray muon flux, at different depths. We demonstrate that a low-temperature underground experiment at a depth of about 6.5 kilometer water equivalent would have a low enough background to allow detection of bulk heating for a collapse rate $\lambda$ of ${10}^{-16}{\mathrm{s}}^{-1}$ using presently available technology.

We investigate the effect of a periodic modulation on parity-time symmetry in a non-Hermitian Rabi model with balanced gain or loss. It is shown that under the multiple-photon resonance conditions, this Rabi model supports exact Floquet solutions for certain special parameter conditions which allow us to find exact analytical results for the position of certain exceptional points (EPs). It is also found numerically that there exists a universal relation between the number of the EPs and the gain or loss strength.

We consider the task of anonymously transmitting a quantum message in a network. We present a protocol that accomplishes this task using the $W$ state and we analyze its performance in a quantum network where some form of noise is present. We then compare the performance of our protocol with some of the existing protocols developed for the task of anonymous transmission. We show that, in many regimes, our protocol tolerates more noise and achieves higher fidelities of the transmitted quantum message than the other ones. Furthermore, we demonstrate that our protocol tolerates one nonresponsive node. We prove the security of our protocol in a semiactive adversary scenario, meaning that we consider an active adversary and a trusted source.

Noncommutativity is one of the most elementary nonclassical features of quantum observables. Here we propose a method to detect noncommutativity of interaction Hamiltonians of two probe objects coupled via a mediator. If these objects are open to their local environments, our method reveals nondecomposability of temporal evolution into a sequence of interactions between each probe and the mediator. The Hamiltonians or Lindblad operators can remain unknown throughout the assessment, we only require knowledge of the dimension of the mediator. Furthermore, no operations on the mediator are necessary. Technically, under the assumption of decomposable evolution, we derive upper bounds on correlations between the probes and then demonstrate that these bounds can be violated with correlation dynamics generated by non-commuting Hamiltonians, e.g., Jaynes-Cummings coupling. An intuitive explanation is provided in terms of multiple exchanges of a virtual particle which lead to the excessive accumulation of correlations. A plethora of correlation quantifiers are helpful in our method, e.g., quantum entanglement, discord, mutual information, and even classical correlation. Finally, we discuss exemplary applications of the method in quantum information: the distribution of correlations and witnessing dimension of an object.

Inspired by the extended Koopmans theorem, we demonstrate that excited electronic states can efficiently and very accurately be computed from the ground-state density correlators. That this is possible in principle does not come as a surprise. However, what correlator order is needed is an important question. There are a number of methods that differ in the way in which higher-order correlators, which are very expensive to evaluate, are treated: the equation-of-motion approach, also known as the random phase approximation, the cumulant, and the Hermitian operator methods. Here it is shown that there exists, in fact, a close connection between the extended Koopmans theorem and the equation-of-motion approach. A dramatic improvement over the conventional linear-response calculations is numerically demonstrated for a paradigmatic molecular system and explained by comparing with the equation-of-motion approach for a single-determinant reference state and for the case of composite excitations. Our approach opens prospects for systematic improvements of the adiabatic approximation of the time-dependent density functional theory by exploiting properties of the correlated ground state.

The off-resonant ac Stark shift for coherent population trapping (CPT) resonances probed with Ramsey spectroscopy is investigated experimentally and theoretically. Measurements with laser-cooled ${}^{87}\mathrm{Rb}$ atoms show excellent quantitative agreement with a simple theory. The shift depends on the relative intensity of the two CPT light fields, but depends only weakly on the total intensity. Since the origin of the shift is through couplings of the interrogation light to off-resonant excited-state hyperfine levels, the size and sign of the shift depend on the specific interrogation scheme. The theory also shows that for several commonly used interrogation schemes it is possible to minimize the off-resonant light shift or its dependence on the CPT intensity ratio by properly selecting the system parameters.

High harmonic generation has been considered for many years to be a coherent source of upconverted laser radiation. We propose a method for the generation of essentially incoherent high harmonic generation with a controlled degree of temporal coherence, obeying random-walk statistics. This is achieved by a unique combination of single-atom and macroscopic effects involving preparation of the medium in an excited state with coordinate-dependent population inversion and using an intense off-resonant and phase-mismatched pumping.

Narrow bright or dark resonances associated with electromagnetically induced transparency play a key role in enhancing photon-photon interactions. The schemes realized to date relied on the existence of long-lived atomic states with strong van der Waals interactions. Here, we show that by placing an atomically thin semiconductor with ultrafast radiative decay rate inside a microcavity, it is possible to obtain extremely narrow dark or bright resonances in transmission. While breaking of translational invariance sets a limit on the width of the dark resonance width, it is possible to obtain a narrow bright resonance that is much narrower than the cavity and bare exciton decay rates and is protected against disorder by tuning the cavity away from the excitonic transition. Resonant excitation of this bright resonance yields strong photon antibunching even in the limit where the interaction strength is arbitrarily smaller than the non-Markovian disorder broadening and the radiative linewidth of the bare exciton. Our findings suggest that atomically thin semiconductors which exhibit large exciton-cavity coupling and small nonradiative line broadening could pave the way for the realization of strongly interacting photonic systems in the solid state.

A scheme for identifying the quantum radiation reaction effect on relativistic electron motion in strong electromagnetic fields is proposed, where two ultraintense lasers are used to collide with each other in a tenuous gas. Different from the previous method by collision of an ultraintense laser with a high-energy electron beam, in which the radiation reaction effect is evidenced by the energy loss in the electron energy spectrum, here the transition between the classical and quantum radiation reaction regimes is distinguished from the angular distribution of the total electron radiations. With no need of additional relativistic electron beams, the scheme is more robust and easily achievable in experiments. Both theory and two-dimensional particle-in-cell simulations show that the classical radiation dominates in the transverse direction perpendicular to laser axis, forming a dipolelike pattern, while that in the quantum regime dominates at four diagonal directions, constituting a butterflylike structure.

One of the most promising routes towards fault-tolerant quantum computation utilizes topological quantum error correcting codes, such as the ${\mathbb{Z}}_2$ surface code. Logical qubits can be encoded in a variety of ways in the surface code, based on either boundary defects, holes, or bulk twist defects. However, proposed fault-tolerant implementations of the Clifford group in these schemes are limited and often require unnecessary overhead. For example, the Clifford phase gate in certain planar and hole encodings has been proposed to be implemented using costly state injection and distillation protocols. In this paper, we show that within any encoding scheme for the logical qubits, we can fault tolerantly implement the full Clifford group by using joint measurements involving a single appropriately encoded logical ancilla. This allows us to provide low overhead implementations of the full Clifford group in surface and color codes. It also provides the first proposed implementations of the full Clifford group in hyperbolic codes. We further use our methods to propose state-of-the art encoding schemes for small numbers of logical qubits; for example, for code distances $d=3,5,7$, we propose a scheme using $60,160,308$ (respectively) physical data qubits, which allow for the full logical Clifford group to be implemented on two logical qubits. To our knowledge, this is the optimal proposal to date, and thus may be useful for demonstration of fault-tolerant logical gates in small near-term quantum computers.

We calculate the nonadiabatic relativistic correction to rovibrational energy levels of ${\mathrm{H}}_2$, ${\mathrm{D}}_2$, and HD molecules using the nonadiabatic perturbation theory. This approach allows one to obtain nonadiabatic corrections to all the molecular levels with the help of a single effective potential. The obtained results are in very good agreement with the previous direct calculation of nonadiabatic relativistic effects for dissociation energies and resolve the reported discrepancies of theoretical predictions with recent experimental results.

We calculate the polarizabilities of the Zeeman sublevels of ${}^{25}\mathrm{Mg}^{+}$ ion hyperfine ground states. To verify the calculation result, a single ${}^{25}\mathrm{Mg}^{+}$ ion is trapped in a Paul trap and a microwave resonance measurement is carried out on the ground states with and without the light shift. A good agreement between the experimental result and the calculation result is obtained.