Chongqing University Team Presents Squeezing-Dicke Model for Non-Hermitian Many-Body Systems

A new Hermitian squeezing-Dicke model, presented by Jun-Ling Wang of Chongqing University and colleagues from Zhejiang University, offers a minimal setting for exploring non-Hermitian behaviour. The model uses a Hermitian quadratic bosonic system to generate effective parity-time ($\mathcal{PT}$) symmetry through squeezing, rather than dissipation. It identifies a non-Hermitian anomalous superradiant phase exhibiting spontaneous $\mathcal{PT}$ symmetry breaking and reveals a dynamical phase transition culminating in quantum amplification with unidirectional enhanced transmission. This provides a new route towards exotic non-Hermitian physics and nonreciprocal quantum phenomena.

Mimicking non-Hermiticity through quantum light squeezing and Hermitian modelling

Squeezing, a fundamental technique in quantum optics, proved central to this approach. It involves reducing the quantum noise in one quadrature of the electromagnetic field at the expense of increased noise in the other, effectively manipulating the uncertainty principle. Rather than inducing non-Hermiticity, a property where energy is not necessarily conserved and the usual rules of quantum mechanics are altered, through typical methods involving energy loss or dissipation, squeezing reshaped the light’s quantum properties. This manipulation effectively created a scenario mimicking gains and losses, similar to a perfectly balanced seesaw in the quantum world, known as parity-time ($\mathcal{PT}$) symmetry. $\mathcal{PT}$ symmetry, in its conventional form, requires a balanced interplay between gain and loss, traditionally achieved through dissipative elements. This research demonstrates that such a balance can be realised purely through quantum squeezing, offering a significant departure from established methodologies.

Careful control of the squeezing interactions allowed construction of a Hermitian squeezing-Dicke model, a simplified theoretical framework representing light and matter interactions, engineered to exhibit these unusual quantum behaviours. The Dicke model traditionally describes the interaction between a single mode of the electromagnetic field and a collection of two-level atoms. By incorporating squeezing, the researchers created a system where the effective Hamiltonian remains Hermitian, despite exhibiting non-Hermitian characteristics. A Holstein-Primakoff transformation and a Bogoliubov transformation were employed to analyse the system. The Holstein-Primakoff transformation maps bosonic operators onto spin operators, simplifying the analysis of many-body systems. The subsequent Bogoliubov transformation diagonalises the Hamiltonian, revealing the excitation spectrum and identifying the conditions for $\mathcal{PT}$ symmetry breaking. This resulted in a Bogoliubov-de Gennes Hamiltonian that was non-Hermitian due to the quadrature interaction terms. Parameters included a squeezing strength, η, and a ferromagnetic interaction strength, γ, both set to 0.35ω, where ω represents the frequency of the cavity mode. This specific parameter choice was crucial for observing the desired non-Hermitian effects. This model enables investigation of non-Hermitian physics without relying on energy loss, utilising squeezing interactions to simulate gains and losses and creating a balanced quantum system. The implications of this approach extend to the exploration of exotic quantum phenomena previously inaccessible without energy dissipation, opening avenues for novel quantum technologies, such as enhanced sensors and non-reciprocal devices.

Hermitian squeezing-Dicke model realises non-Hermitian amplification and unidirectional transmission

A key coupling strength of λNP c has been achieved, representing a strong improvement over previous methods limited to dissipation-induced non-Hermiticity. This breakthrough unlocks the exploration of exotic quantum phenomena previously inaccessible without energy dissipation. Previous approaches to realising non-Hermiticity often relied on weak coupling between the system and its environment, limiting the observable effects. This new model demonstrates a significantly stronger coupling, allowing for more pronounced and readily observable non-Hermitian behaviour. System analysis revealed a non-Hermitian anomalous superradiant phase exhibiting spontaneous parity-time ($\mathcal{PT}$) symmetry breaking, characterised by complex excitation spectra and a dynamical phase transition. Superradiance, a collective emission of photons from multiple atoms, is enhanced and modified in this non-Hermitian regime, leading to the anomalous phase. The spontaneous $\mathcal{PT}$ symmetry breaking signifies a qualitative change in the system’s behaviour, where the symmetry is no longer preserved.

The combination of an artificial magnetic field and broken Hermiticity yields nonreciprocal dynamics with striking quantum amplification, demonstrating unidirectional enhanced transmission. Non-reciprocity, the property of transmitting signals preferentially in one direction, is a crucial feature for building isolators and circulators in quantum circuits. The critical coupling strength was identified as 1/2s (ω + 2γ) (ω² −4η²) / (ω −2η cos 2θ), where ω represents cavity frequency and η signifies the strength of two-photon squeezing; the system remains in a normal phase below this value. This equation defines the threshold at which the $\mathcal{PT}$ symmetry breaks and the non-Hermitian effects become dominant. The energy spectrum revealed a modified parity-time symmetry, even with a non-zero magnetic flux, separating gain and loss on opposite sides. This spatial separation of gain and loss is a hallmark of $\mathcal{PT}$ symmetry and contributes to the observed unidirectional transmission.

Achieving non-Hermiticity in quantum systems through light state manipulation

Manipulating light to control quantum systems is well established, but achieving non-Hermiticity, a condition where energy isn’t necessarily conserved, has traditionally demanded introducing energy loss. The Hermitian squeezing-Dicke model offers a compelling alternative, sidestepping dissipation by using precise manipulation of light’s quantum state via squeezing, which alters the uncertainty in light’s properties. Researchers from Chongqing University and Zhejiang University revealed a new way to create non-Hermitian physics within light-matter interactions. This approach reveals an anomalous superradiant phase, a state where light and matter amplify each other, and breaks a specific type of symmetry known as parity-time symmetry, leading to unusual energy levels. The ability to engineer non-Hermiticity without dissipation is particularly significant because dissipation often introduces unwanted noise and decoherence, hindering the performance of quantum devices. Consequently, this offers a pathway to explore quantum phenomena without the limitations imposed by energy dissipation, potentially leading to advancements in quantum information processing and sensing. Specifically, the unidirectional transmission achieved in this model could be exploited to create robust quantum communication channels, while the enhanced amplification could improve the sensitivity of quantum sensors.

Researchers demonstrated a new method for achieving non-Hermiticity in quantum systems by manipulating the quantum state of light through squeezing, rather than relying on energy loss. This work reveals an anomalous superradiant phase and breaks parity-time symmetry within light-matter interactions, resulting in unusual energy levels and unidirectional transmission. The ability to create these effects without energy dissipation is important because dissipation can introduce unwanted noise into quantum systems. The authors suggest this approach provides an alternative route to explore exotic quantum phenomena and potentially improve quantum technologies.