# Quantum Optics of Quantum Many-Body Systems

**Quantum optics of ultracold quantum gases:***Studying the ultimate quantum level of the light-matter interaction*

**Post-doc:** Santiago Caballero Benitez**PhD students:** Wojciech Kozlowski, Gabriel Mazzucchi, Thomas Elliott, Felix Tennie

(See the **GROUP PHOTO** below.)

*RECENT PAPERS:*

Phys. Rev. Lett.-1 (2015), Phys. Rev. Lett.-2 (2015), New J. Phys. (2015), Phys. Rev. A (2015), Atoms (2015), Scientific Reports (2016), New J. Phys.-1 (2016), Phys. Rev. A-1 (2016), Phys. Rev. A-2 (2016), Phys. Rev. A-3 (2016), Phys. Rev. A-4 (2016), arXiv:1601.02230, New J. Phys.-2 (2016), Optica (OSA) (2016), Scientific Reports (2017).

** A REVIEW PAPER** is available at Journ. Phys. B 45, 102001 (2012) (arXiv:1203.0552)

*RECENT RESULTS:*

- We develop a concept of
**"quantum optical lattices,"**where the quantized light creates fully quantum and dynamical trapping potential for ultracold bosons and fermions. - We have introduced the quantum measurement into a many-body system. We have shown that
**the quantum backaction of weak (non-projective) measurement can effeciently compete with unitary dynamics, thus, constituting a novel source of the competitions in many-body systems.**This leads to a plethora of novel effects such as the giant oscillations at single quantum trajectories, long-range correlated pair tunneling, Raman-like virtual transitions in quantum Zeno subspaces, measurement-induced protection and break-up of fermion pairs, and measurement-induced antiferromagnetic orders. **We have suggested quantum simulations based on the collective enhancement of light-matter interaction.**We demonstrated the emergence of not only density orders (e.g., density waves and supersolids), but also the orders of matter-wave coherences (bond orders). This is well beyond predictions of standard Dicke and Bose-Hubbard models.

### RESEARCH HIGHLIGHTS

**Phys. Rev. A (2015):**

The light is not only sensitive to the density correlations, but also reflects the **matter-field interference at its shortest possible distance** in an optical lattice.

Light scattering distinguishes all quantum phases in the Bose Glass - Mott insulator - superfluid phase transition.

**Phys. Rev. Lett.-1 (2015):**

We have shown, how to generate multiple **spatial modes of matter fields** using the quantum measurement. The modes have nontrivial spatial overlap, display **genuine multipartite entanglement**, and can be used for **measurement and detection of the entanglement** in quantum gases. We demonstrate non-Gaussian generalizations of multimode squeezed, parametric down-conversion, and Dicke states.

**Phys. Rev. Lett.-2 (2015):**

We demonstrated novel phase transitions solely due to the quantum light-matter correlations in a **quantum optical lattice**. The competition between light-field and matter-field coherences leads to novel phases (e.g. delocalized dimers), beyond density-induced orders such as multimode generalizations of density waves and supersolid states.

**New J. Phys. (2015):**

We demonstrated that light scattered from novel phases of atoms in **quantum optical lattices** has essentially **nonclassical properties** (e.g. squeezing).

**Atoms (2015), Special Issue:**

We considered quantum nondemolition measurement of many-body states of strongly interacting and non-interacting fermions in optical lattices, and demonstrated the measurement-induced entanglement of spin components and generation of macroscopic superposition states on a lattice. We showed that the quadrature measurements can produce Schrödinger cat states, which are more robust with respect to photon losses, than those obtained by the photon number detection. We also showed that quantum optical lattices generated in a cavity change quantum phases of ultracold bosons.

**Phys. Rev. A-1 (2016):**

We presented a general framework to describe **the competition between global quantum measurement and standard local processes** (tunneling and on-site interaction) in a strongly correlated many-body system. We demonstrated **the following new phenomena**: design of nonlocal spatially structured environment for otherwise closed many-body system, long-range correlated tunneling, nonlocal quantum Zeno effect, generation of multimode Schrödinger cat states, break-up and protection of strongly interacting fermion pairs.

**Phys. Rev. A-2 (2016):**

We suggested a novel type of quantum simulators based on the collective enhancement of light-matter interactions.

**New J. Phys.-1 (2016):**

We predicted a nontrivial type of dynamics resulting from the novel competition between the quantum backaction of weak measurement and unitary many-body (or multimode) dynamics.

**Phys. Rev. A-3 (2016):**

We have extended the notion of **quantum Zeno dynamics** in the realm of **non-Hermitian processes**. Moreover, we presented an unconventional scenario for quantum Zeno dynamics: a system evolves within a Zeno subspace thanks to Raman-like transitions via virtual states outside that subspace. This corresponds to a rather strong, but not projective quantum measurement.

**Scientific Reports (2016):**

We demonstrated how the quantum backaction of weak continuous measurement can lead to the **generation of antiferromagnetic order and density modulations** in the system of ultracold fermions in optical lattices.

**Phys. Rev. A-4 (2016):**

We demonstrated that joining the ideas of quantum measurement and quantum optical lattices can broaden the field of quantum simulations, allowing simulating numerous models such as superexchange interactions, multispecies Dicke model, pair creation and annihilation, dynamical gauge fields, etc.

**arXiv:1601.02230:**

We demonstrated that the quantum feedback control can strongly influence the stability region of a BEC trapped inside a cavity. Moreover, it can be used to precisely position a BEC in space and tune the phase of the generated light.

**New J. Phys.-2 (2016):**

We showed that the emergent **global bond order** (i.e. the self-organization of matter-wave coherences, rather than densities) is linked to the **valence bond solids (VBS)**. This opens a novel avenue for **global quantum simulations**, in particular, of high-Tc superconductors.

**Optica (OSA) (2016):**

We have described the quantum feedback control of novel many-body states, which appear as a result of the competition between the weak measurement backaction and many-body dynamics: multimode density waves and supersolids, antiferromagnetic and NOON states.

**Scientific Reports (2017):**

Instead of coupling light to the atomic on-site density, we propose a method of coupling directly to the **matter-phase-related variables**. This constitutes a novel type of quantum measurements and projections, thus **generalizing the standard measurement postulate** for the case of competition between the weak measurement backaction and system's own dynamics.

### NEWS

*Visit by Professor Peter Domokos (Wigner Research Centre for Physics, Budapest)**Visit by Dr. Denis Ivanov (St. Petersburg State University)**Visit by Professor Janne Ruostekoski (University of Southampton)**Visit by Professor Michael Hartmann (Heriot-Watt University, Edinburgh)**Visit by Professor Jacob Sherson (Aarhus University)**Welcome to Santiago Caballero Benitez, who has started his postdoc!**Visit by Professor Guangjiong Dong (East China Normal University, Shanghai)**Welcome to a new graduate student Thomas Elliott!**Visit by Professor Claus Zimmermann (University of Tübingen)**A REVIEW paper is available at Journ. Phys. B 45, 102001 (2012) (arXiv:1203.0552)**Visit by Dr. Vincent Boyer (University of Birmingham)**Wojciech Kozlowski, Gabriel Mazzucchi and Felix Tennie have joined the group as graduate students.*

### RESEARCH DESCRIPTION

**Theoretical quantum optics of ultracold quantum gases**

*Studying the ultimate quantum limit of the light-matter interaction*

** A REVIEW PAPER ** is available at Journ. Phys. B 45, 102001 (2012) (arXiv:1203.0552)

Both quantum optics and many-body physics of the lowest achievable temperatures are very active fields of modern research. However, the interaction between them is far from being complete.

In the most theoretical and experimental works on ultracold atoms, the role of light is reduced to a classical tool for preparing intriguing atomic states. In contrast, the main goal of this research is to develop a theory of the phenomena, where the quantum natures of both ultracold matter and light play equally important roles.

This research will close the gap between quantum optics and physics of ultracold quantum matter, considering the ultimate quantum regime of the light-matter interaction. The experiments on this regime became possible just several years ago, which makes the interaction between the theory and experiment promising.

**First**, the quantized light serves as a **quantum nondemolition (QND) probe** sensitive to the quantum states of ultracold particles. The applications exist for ultracold **atomic gases** (Nature Physics (2007), Phys. Rev. Lett. (2007), Phys. Rev. A (2007), Laser Physics (2009)), **polar molecules** (Phys. Rev. Lett. (2011), Phys. Rev. A (2011), Laser Physics (2013)) and other systems as well.

In a **recent paper** (Phys. Rev. A (2015)), we proved that light is not only sensitive to the density correlations, but also reflects the **matter-field interference at its shortest possible distance** in an optical lattice. We also showed, how to distinguish the Bose Glass, Mott insulator and superfluid phases.

**Second**, due to the light-matter entanglement, the **quantum measurement-based preparation of many-body atomic states** is possible. The class of emerging atomic states can be chosen via optical geometry, thus, the light scattering constitutes a quantum measurement with a controllable form of the measurement back-action. For example, the **atom number squeezed and Schrödinger cat states** can be prepared. (Phys. Rev. Lett. (2009), Phys. Rev. A (2009), Laser Physics (2010), Laser Phys. (2011))

In a **recent paper** (Phys. Rev. Lett.-1 (2015)), we have shown, how to generate multiple **spatial modes of matter fields** using the quantum measurement. The modes have nontrivial spatial overlap, display **genuine multipartite entanglement**, and can be used for **measurement and detection of the entanglement** in quantum gases.

Moreover, in Phys. Rev. A-1 (2016) we presented a general framework to describe **the competition between global quantum measurement and standard local processes** (tunneling and on-site interaction) in a strongly correlated many-body system. We demonstrated **the following new phenomena**: design of nonlocal spatially structured environment for otherwise closed many-body system, long-range correlated tunneling, nonlocal quantum Zeno effect, generation of multimode Schrödinger cat states, break-up and protection of strongly interacting fermion pairs.

In Atoms (2015) we have shown the measurement-induced entanglement between fermion spin components on a lattice, and showed that the homodyne detection can produce more robust states, than those produced by photon number measurements.

In Phys. Rev. A-3 (2016), we have extended the notion of **quantum Zeno dynamics** in the realm of **non-Hermitian processes**. Moreover, we presented an unconventional scenario for quantum Zeno dynamics: a system evolves within a Zeno subspace thanks to Raman-like transitions via virtual states outside that subspace. This corresponds to a rather strong, but not projective quantum measurement.

In Scientific Reports (2016), we demonstrated how the quantum backaction of weak continuous measurement can lead to the **generation of antiferromagnetic order and density modulations** in the system of ultracold fermions in optical lattices.

In Phys. Rev. A-4 (2016), we demonstrated that joining the ideas of quantum measurement and quantum optical lattices can broaden the field of quantum simulations, allowing simulating numerous models such as superexchange interactions, multispecies Dicke model, pair creation and annihilation, dynamical gauge fields, etc.

In arXiv:1601.02230 we demonstrated that the quantum feedback control can strongly influence the stability region of a BEC trapped inside a cavity. Moreover, it can be used to precisely position a BEC in space and tune the phase of the generated light.

In New J. Phys.-1 (2016), we predicted a nontrivial type of dynamics resulting from the novel competition between the quantum backaction of weak measurement and unitary many-body (or multimode) dynamics.

In Optica (OSA) (2016), we have described the quantum feedback control of novel many-body states, which appear as a result of the competition between the weak measurement backaction and many-body dynamics: multimode density waves and supersolids, antiferromagnetic and NOON states.

In Scientific Reports (2017), instead of coupling light to the atomic on-site density, we propose a method of coupling directly to the **matter-phase-related variables**. This constitutes a novel type of quantum measurements and projections, thus **generalizing the standard measurement postulate** for the case of competition between the weak measurement backaction and system's own dynamics.

**Third**, trapping atoms inside an optical cavity one creates the light potential, which is a quantized and dynamical variable itself, rather a prescribed classical function as it is usual in the quantum gas problems. In the cavity QED with quantum gases, the self-consistent solution for light and particles is required, which enriches the picture of **quantum many-body states of atoms trapped in quantum potentials**. (Eur. Phys. Journal D (2008), Phys. Rev. A (2007))

In a **recent paper** (Phys. Rev. Lett.-2 (2015)), we demonstrated novel phase transitions solely due to the quantum light-matter correlations in a **quantum optical lattice**.

Moreover, we showed the generation of nonclassical light (e.g. squeezed) in such systems (New J. Phys. (2015)).

In Phys. Rev. A-2 (2016), we proposed a new type of quantum simulators based on the collective enhancement of light-matter interactions.

In New J. Phys.-2 (2016), we showed that the emergent **global bond order** (i.e. the self-organization of matter-wave coherences, rather than densities) is linked to the **valence bond solids (VBS)**. This opens a novel avenue for **global quantum simulations**, in particular, of high-Tc superconductors.

The application of those fully quantum models to the systems of **semiconductor nanophotonics** are of interest as well.

### Group photos

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